Nonlinear Sciences
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 [1] arXiv:2406.12922 [pdf, html, other]

Title: Chaotic dynamics creates and destroys branched flowSubjects: Pattern Formation and Solitons (nlin.PS); Chaotic Dynamics (nlin.CD)
The phenomenon of branched flow, visualized as a chaotic arborescent pattern of propagating particles, waves, or rays, has been identified in disparate physical systems ranging from electrons to tsunamis, with periodic systems only recently being added to this list. Here, we explore the laws governing the evolution of the branches in periodic potentials. On one hand, we observe that branch formation follows a similar pattern in all nonintegrable potentials, no matter whether the potentials are periodic or completely irregular. Chaotic dynamics ultimately drives the birth of the branches. On the other hand, our results reveal that for periodic potentials the decay of the branches exhibits new characteristics due to the presence of infinitely stable branches known as superwires. Again, the interplay between branched flow and superwires is deeply connected to Hamiltonian chaos. In this work, we explore the relationships between the laws of branched flow and the structures of phase space, providing extensive numerical and theoretical arguments to support our findings.
 [2] arXiv:2406.13320 [pdf, html, other]

Title: Electromagnetic breathing dromionlike structures in an anisotropic ferromagnetic mediumComments: Accepted for publication in Journal of Magnetism and Manetic MaterialsSubjects: Pattern Formation and Solitons (nlin.PS); Other Condensed Matter (condmat.other); Exactly Solvable and Integrable Systems (nlin.SI)
The influence of Gilbert damping on the propagation of electromagnetic waves (EMWs) in an anisotropic ferromagnetic medium is investigated theoretically. The interaction of the magnetic field component of the electromagnetic wave with the magnetization of a ferromagnetic medium has been studied by solving the associated Maxwell's equations coupled with a LandauLifshitzGilbert (LLG) equation. When small perturbations are made on the magnetization of the ferromagnetic medium and magnetic field along the direction of propagation of electromagnetic wave by using the reductive perturbation method, the associated nonlinear dynamics is governed by a timedependent damped derivative nonlinear Schrodinger (TDDNLS) equation. The Lagrangian density function is constructed by using the variational method to solve the TDDNLS equation to understand the dynamics of the system under consideration. The propagation of EMW in a ferromagnetic medium with inherent Gilbert damping admits very interesting nonlinear dynamical structures. These structures include Gilbert dampingmanaging symmetrically breathing solitons, localized erupting electromagnetic breathing dromionlike modes of excitations, breathing dromionlike soliton, decaying dromionlike modes and an unexpected creationannihilation mode of excitations in the form of growingdecaying dromionlike modes.
 [3] arXiv:2406.13383 [pdf, html, other]

Title: Emergent Dynamics in Heterogeneous LifeLike Cellular AutomataAarati Shrestha, Felix Reimers, Sanyam Jain, Paolo Baldini, Michele Braccini, Andrea Roli, Stefano NicheleComments: 16 pages, 9 FiguresSubjects: Cellular Automata and Lattice Gases (nlin.CG); Emerging Technologies (cs.ET)
The Game of Life (GoL), one well known 2D cellular automaton, does not typically ensure interesting longterm phenotypic dynamics. Therefore, while being Turing complete, GoL cannot be said to be openended. In this work, we extend GoL with the opportunity for local mutations, thus enabling a heterogeneous lifelike cellular automaton guided by an evolutionary inner loop. Additionally, we introduce the concept of cell ageing to ensure that cell aliveness (activated by inheritance with variation, and controlled by ageing) and actual cell computation (governed by lifelike rules on local neighborhoods) are kept conceptually separated. We conduct an experimental campaign to identify suitable parameters that produce longterm phenotypic dynamics and favor genotypic innovations.
 [4] arXiv:2406.13423 [pdf, html, other]

Title: Lagrangian multiform structure of discrete and semidiscrete KP systemsComments: 25 pages, 1 figureSubjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (mathph)
A variational structure for the potential AKP system is established using the novel formalism of a Lagrangian multiforms. The structure comprises not only the fully discrete equation on the 3D lattice, but also its semidiscrete variants including several differentialdifference equations asssociated with, and compatible with, the partial difference equation. To this end, an overview is given of the various (discrete and semidiscrete) variants of the KP system, and their associated Lax representations, including a novel `generating PDE' for the KP hierarchy. The exterior derivative of the Lagrangian 3form for the lattice potential KP equation is shown to exhibit a doublezero structure, which implies the corresponding generalised EulerLagrange equations. Alongside the 3form structures, we develop a variational formulation of the corresponding Lax systems via the square eigenfunction representation arising from the relevant direct linearization scheme.
 [5] arXiv:2406.13459 [pdf, html, other]

Title: The RiemannHilbert approach for the nonlocal derivative nonlinear Schr\"odinger equation with nonzero boundary conditionsSubjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (mathph)
In this paper, the nonlocal reverse spacetime derivative nonlinear Schrödinger equation under nonzero boundary conditions is investigated using the RiemannHilbert (RH) approach. The direct scattering problem focuses on the analyticity, symmetries, and asymptotic behaviors of the Jost eigenfunctions and scattering matrix functions, leading to the construction of the corresponding RH problem. Then, in the inverse scattering problem, the Plemelj formula is employed to solve the RH problem. So the reconstruction formula, trace formulae, $\theta$ condition, and exact expression of the singlepole and doublepole solutions are obtained. Furthermore, darkdark solitons, brightdark solitons, and breather solutions of the reverse spacetime derivative nonlinear Schrödinger equation are presented along with their dynamic behaviors summarized through graphical simulation.
 [6] arXiv:2406.13701 [pdf, html, other]

Title: Windwave interaction in finite depth: linear and nonlinear approaches, blowup and soliton breaking in finite time, integrability perspectivesSubjects: Pattern Formation and Solitons (nlin.PS); Mathematical Physics (mathph)
This work is an analytical investigation of the evolution of surface water waves in Miles and Jeffreys theories of wind wave interaction in water of finite depth. The present review is divided into two major parts. The first corresponds to the surface water waves in a linear regime and its nonlinear extensions. In this part, Miles theory of wave amplification by wind is extended to the case of finite depth. The dispersion relation provides a wave growth rate depending on depth. Our theoretical results are in good agreement with the data from the Australian Shallow Water Experiment and the data from the Lake George experiment. In the second part of this study, Jeffreys theory of wave amplification by wind is extended to the case of finite depth, where the SerreGreenNaghdi is derived. We find the solitary wave solution of the system, with an increasing amplitude under the action of the wind. This continuous increase in amplitude leads to the soliton breaking and blowup of the surface wave in finite time. The theoretical blowup time is calculated based on actual experimental data. By applying an appropriate perturbation method, the SGN equation yields Korteweg de Vries Burger equation (KdVB). We show that the continuous transfer of energy from wind to water results in the growth of the KdVB soliton amplitude, velocity, acceleration, and energy over time while its effective wavelength decreases. This phenomenon differs from the classical results of Jeffreys approach due to finite depth. Again, blowup and breaking occur in finite time. These times are calculated and expressed for soliton and windappropriate parameters and values. These values are measurable in usual experimental facilities. The kinematics of the breaking is studied, and a detailed analysis of the breaking time is conducted using various criteria. Finally, some integrability perspectives are presented.
New submissions for Friday, 21 June 2024 (showing 6 of 6 entries )
 [7] arXiv:2406.12852 (crosslist from math.GM) [pdf, other]

Title: Analyzing Dynamical Systems Inspired by Montgomery's Conjecture: Insights into Zeta Function Zeros and Chaos in Number TheoryComments: 37pages,14figure,4tablesSubjects: General Mathematics (math.GM); Chaotic Dynamics (nlin.CD)
In this study, we delve into a novel dynamic system inspired by Montgomery's pair correlation conjecture in number theory. The dynamic system is intricately designed to emulate the behavior of the nontrivial zeros of the Riemann zeta function. Our exploration encompasses bifurcation analysis and Lyapunov exponents to scrutinize the system's behavior and stability, offering insights into both small and large initial conditions. Our efforts extend to unveiling the probability distribution characterizing the dynamics for varying initial conditions. The dynamic system unfolds intricate behaviors, displaying sensitivity to initial conditions and revealing complex bifurcation patterns. Small deviations in the initial conditions unveil significantly different trajectories, reminiscent of chaotic systems. Lyapunov exponents become our lens into understanding stability and chaos within the system. A comparative analysis between the dynamic system's approximate solutions and the actual nontrivial zeros of the Riemann zeta function enhances our comprehension of model accuracy and its potential implications for number theory.
This research illuminates the versatility of dynamic systems as analogs for studying complex mathematical phenomena. It provides fresh perspectives on the pair correlation conjecture, establishing connections with nonlinear dynamics and chaos theory. Notably, we delve into the boundedness of solutions for both small and large initial conditions, unraveling the distinctive probability distribution governing the dynamics in each scenario. Furthermore, we introduce an indepth analysis of the entropy of our dynamic system for both small and large initial conditions. The entropy study enhances our understanding of the predictability and stability of the system, shedding light on its behavior in different parameter regimes.  [8] arXiv:2406.12895 (crosslist from qbio.NC) [pdf, html, other]

Title: Temporal Complexity of a HopfieldType Neural Model in Random and ScaleFree GraphsSubjects: Neurons and Cognition (qbio.NC); Disordered Systems and Neural Networks (condmat.disnn); Mathematical Physics (mathph); Numerical Analysis (math.NA); Adaptation and SelfOrganizing Systems (nlin.AO)
The Hopfield network model and its generalizations were introduced as a model of associative, or contentaddressable, memory. They were widely investigated both as a unsupervised learning method in artificial intelligence and as a model of biological neural dynamics in computational neuroscience. The complexity features of biological neural networks are attracting the interest of scientific community since the last two decades. More recently, concepts and tools borrowed from complex network theory were applied to artificial neural networks and learning, thus focusing on the topological aspects. However, the temporal structure is also a crucial property displayed by biological neural networks and investigated in the framework of systems displaying complex intermittency. The IntermittencyDriven Complexity (IDC) approach indeed focuses on the metastability of selforganized states, whose signature is a powerdecay in the interevent time distribution or a scaling behavior in the related eventdriven diffusion processes. The investigation of IDC in neural dynamics and its relationship with network topology is still in its early stages. In this work we present the preliminary results of a IDC analysis carried out on a bioinspired Hopfieldtype neural network comparing two different connectivities, i.e., scalefree vs. random network topology. We found that random networks can trigger complexity features similar to that of scalefree networks, even if with some differences and for different parameter values, in particular for different noise levels.
 [9] arXiv:2406.12906 (crosslist from qbio.NC) [pdf, other]

Title: Entropystatistical approach to phaselocking detection of pulse oscillations: application for the analysis of biosignal synchronizationComments: 23 pages, 12 figures, 3 tablesSubjects: Neurons and Cognition (qbio.NC); Machine Learning (cs.LG); Adaptation and SelfOrganizing Systems (nlin.AO)
In this study a new method for analyzing synchronization in oscillator systems is proposed using the example of modeling the dynamics of a circuit of two resistively coupled pulse oscillators. The dynamic characteristic of synchronization is fuzzy entropy (FuzzyEn) calculated a time series composed of the ratios of the number of pulse periods (subharmonic ratio, SHR) during phaselocking intervals. Low entropy values indicate strong synchronization, whereas high entropy values suggest weak synchronization between the two oscillators. This method effectively visualizes synchronized modes of the circuit using entropy maps of synchronization states. Additionally, a classification of synchronization states is proposed based on the dependencies of FuzzyEn on the length of embedding vectors of SHR time series. An extension of this method for analyzing nonrelaxation (nonspike) type signals is illustrated using the example of phasephase coupling rhythms of local field potential of rat hippocampus. The entropystatistical approach using rational fractions and pulse signal forms makes this method promising for analyzing biosignal synchronization and implementing the algorithm in mobile digital platforms.
 [10] arXiv:2406.12948 (crosslist from cs.CR) [pdf, other]

Title: New Reservoir Computing Kernel Based on Chaotic Chua Circuit and Investigating Application to PostQuantum CryptographyComments: 72 pages, 62 figures, Master of Engineering final project reportSubjects: Cryptography and Security (cs.CR); Machine Learning (cs.LG); Chaotic Dynamics (nlin.CD); Applied Physics (physics.appph); Classical Physics (physics.classph)
The aim of this project was to develop a new Reservoir Computer implementation, based on a chaotic Chua circuit. In addition to suitable classification and regression benchmarks, the Reservoir Computer was applied to PostQuantum Cryptography, with its suitability for this application investigated and assessed. The cryptographic algorithm utilised was the Learning with Errors problem, for both encryption and decryption. To achieve this, the Chua circuit was characterised, in simulation, and by physical circuit testing. The Reservoir Computer was designed and implemented using the results of the characterisation. As part of this development, noise was considered and mitigated.
The benchmarks demonstrate that the Reservoir Computer can achieve current literature benchmarks with low error. However, the results with Learning with Errors suggest that a Chuabased Reservoir Computer is not sufficiently complex to tackle the high nonlinearity in PostQuantum Cryptography. Future work would involve researching the use of different combinations of multiple Chua Reservoir Computers in larger neural network architectures. Such architectures may produce the required highdimensional behaviour to achieve the Learning with Errors problem.
This project is believed to be only the second instance of a Chuabased Reservoir Computer in academia, and it is the first to be applied to challenging realworld tasks such as PostQuantum Cryptography. It is also original by its investigation of hitherto unexplored parameters, and their impact on performance. It demonstrates a proofofconcept for a massproducible, inexpensive, lowpower consumption hardware neural network. It also enables the next stages in research to occur, paving the road for using Chuabased Reservoir Computers across various applications.  [11] arXiv:2406.13101 (crosslist from cs.LG) [pdf, html, other]

Title: On instabilities in neural networkbased physics simulatorsComments: 15 pagesSubjects: Machine Learning (cs.LG); Computational Engineering, Finance, and Science (cs.CE); Chaotic Dynamics (nlin.CD)
When neural networks are trained from data to simulate the dynamics of physical systems, they encounter a persistent challenge: the longtime dynamics they produce are often unphysical or unstable. We analyze the origin of such instabilities when learning linear dynamical systems, focusing on the training dynamics. We make several analytical findings which empirical observations suggest extend to nonlinear dynamical systems. First, the rate of convergence of the training dynamics is uneven and depends on the distribution of energy in the data. As a special case, the dynamics in directions where the data have no energy cannot be learned. Second, in the unlearnable directions, the dynamics produced by the neural network depend on the weight initialization, and common weight initialization schemes can produce unstable dynamics. Third, injecting synthetic noise into the data during training adds damping to the training dynamics and can stabilize the learned simulator, though doing so undesirably biases the learned dynamics. For each contributor to instability, we suggest mitigative strategies. We also highlight important differences between learning discretetime and continuoustime dynamics, and discuss extensions to nonlinear systems.
 [12] arXiv:2406.13147 (crosslist from cs.MA) [pdf, html, other]

Title: A Simulation Environment for the Neuroevolution of Ant Colony DynamicsComments: Accepted for publication at The 2024 Conference on Artificial Life. 2 page extended abstractSubjects: Multiagent Systems (cs.MA); Neural and Evolutionary Computing (cs.NE); Adaptation and SelfOrganizing Systems (nlin.AO)
We introduce a simulation environment to facilitate research into emergent collective behaviour, with a focus on replicating the dynamics of ant colonies. By leveraging realworld data, the environment simulates a target ant trail that a controllable agent must learn to replicate, using sensory data observed by the target ant. This work aims to contribute to the neuroevolution of models for collective behaviour, focusing on evolving neural architectures that encode domainspecific behaviours in the network topology. By evolving models that can be modified and studied in a controlled environment, we can uncover the necessary conditions required for collective behaviours to emerge. We hope this environment will be useful to those studying the role of interactions in emergent behaviour within collective systems.
 [13] arXiv:2406.13442 (crosslist from condmat.soft) [pdf, html, other]

Title: Designing necks and wrinkles in inflated auxetic membranesJournalref: International Journal of Mechanical Sciences 268 (2024) 109031Subjects: Soft Condensed Matter (condmat.soft); Pattern Formation and Solitons (nlin.PS)
This article presents the potentiality of inflatable, functionallygraded auxetic membranes to produce wrinkles and necks. We obtain elastic instabilities at desired locations in axisymmetric membranes and with prescribed patterns in square membranes. First, we use an analytical approach to obtain a series of universal results providing insights into the formation of wrinkles and necks in inflated, axisymmetric membranes. For example, we prove analytically that necks and wrinkles may never overlap in pressurized, axially symmetric membranes. Second, we implement the relaxed strain energy of tension field theory into a Finite Element solver (COMSOL). By tuning spatial inhomogeneities of the material moduli, we corroborate our universal results, describe the onset of wrinkling in an averaged way, and also generate nontrivial instabilities at desired locations. This study on membranes with morphing or corrugation on demand has potential applications in Braille reading and haptics.
 [14] arXiv:2406.13483 (crosslist from condmat.soft) [pdf, html, other]

Title: Voltagecontrolled nonaxisymmetric vibrations of soft electroactive tubes with strainstiffening effectJournalref: International Journal of Solids and Structures 290 (2024) 112671Subjects: Soft Condensed Matter (condmat.soft); Pattern Formation and Solitons (nlin.PS)
Material properties of soft electroactive (SEA) structures are significantly sensitive to external electromechanical biasing fields (such as prestretch and electric stimuli), which generate remarkable knockon effects on their dynamic characteristics. In this work, we analyze the electrostatically tunable nonaxisymmetric vibrations of an incompressible SEA cylindrical tube under the combination of a radially applied electric voltage and an axial prestretch. Following the theory of nonlinear electroelasticity and the associated linearized theory for superimposed perturbations, we derive the nonlinear static response of the SEA tube to the inhomogeneous biasing fields for the Gent ideal dielectric model. Using the State Space Method, we efficiently obtain the frequency equations for voltagecontrolled smallamplitude threedimensional nonaxisymmetric vibrations, covering a wide range of behaviors, from the purely radial breathing mode to torsional modes, axisymmetric longitudinal modes, and prismatic diffuse modes. We also perform an exhaustive numerical analysis to validate the proposed approach compared with the conventional displacement method, as well as to elucidate the influences of the applied voltage, axial prestretch, and strainstiffening effect on the nonlinear static response and vibration behaviors of the SEA tube. The present study clearly indicates that manipulating electromechanical biasing fields is a feasible way to tune the smallamplitude vibration characteristics of an SEA tube. The results should benefit experimental work on, and design of, voltagecontrolled resonant devices made of SEA tubes.
 [15] arXiv:2406.13503 (crosslist from mathph) [pdf, html, other]

Title: Integrable $\mathbb{Z}_2^2$graded Extensions of the Liouville and SinhGordon TheoriesComments: 25 pagesSubjects: Mathematical Physics (mathph); High Energy Physics  Theory (hepth); Exactly Solvable and Integrable Systems (nlin.SI)
In this paper we present a general framework to construct integrable $\mathbb{Z}_2^2$graded extensions of classical, twodimensional Toda and conformal affine Toda theories. The scheme is applied to define the extended Liouville and SinhGordon models; they are based on $\mathbb{Z}_2^2$graded color Lie algebras and their fields satisfy a parabosonic statististics. The mathematical tools here introduced are the $\mathbb{Z}_2^2$graded covariant extensions of the Lax pair formalism and of the Polyakov's soldering procedure. The $\mathbb{Z}_2^2$graded SinhGordon model is derived from an affine $\mathbb{Z}_2^2$graded color Lie algebra, mimicking a procedure originally introduced by BabelonBonora to derive the ordinary SinhGordon model. The color Lie algebras under considerations are: the $6$generator $\mathbb{Z}_2^2$graded $sl_2$, the $\mathbb{Z}_2^2$graded affine ${\widehat{sl_2}}$ algebra with two central extensions, the $\mathbb{Z}_2^2$graded Virasoro algebra obtained from a Hamiltonian reduction.
 [16] arXiv:2406.13504 (crosslist from condmat.statmech) [pdf, html, other]

Title: Selforganized transport in noisy dynamic networksComments: 12 pages, 10 figuresSubjects: Statistical Mechanics (condmat.statmech); Adaptation and SelfOrganizing Systems (nlin.AO); Biological Physics (physics.bioph); Neurons and Cognition (qbio.NC)
We present a numerical study of multicommodity transport in a noisy, nonlinear network. The nonlinearity determines the dynamics of the edge capacities, which can be amplified or suppressed depending on the local current flowing across an edge. We consider network selforganization for three different nonlinear functions: For all three we identify parameter regimes where noise leads to selforganization into more robust topologies, that are not found by the sole noiseless dynamics. Moreover, the interplay between noise and specific functional behavior of the nonlinearity gives rise to different features, such as (i) continuous or discontinuous responses to the demand strength and (ii) either single or multistable solutions. Our study shows the crucial role of the activation function on noiseassisted phenomena.
 [17] arXiv:2406.13811 (crosslist from condmat.soft) [pdf, html, other]

Title: Seasonal footprints on ecological time series and jumps in dynamic states of protein configurations from a nonlinear forecasting method characterizationLeonardo Reyes, Kilver Campos, Douglas Avendaño, Lenin GonzálezPaz, Alejandro Vivas, Ysaías J. Alvarado, Saúl FloresComments: 5 pages, 8 figuresSubjects: Soft Condensed Matter (condmat.soft); Adaptation and SelfOrganizing Systems (nlin.AO)
We have analyzed phenology data and jumps in protein configurations with the nonlinear forecasting method proposed by May and Sugihara \cite{MS90}. Full plots of prediction quality as a function of dimensionality and forecasting time give fast and valuable information about Complex Systems dynamics.
 [18] arXiv:2406.13971 (crosslist from cs.LG) [pdf, html, other]

Title: Complex fractal trainability boundary can arise from trivial nonconvexityComments: 11 pages, 9 figures, preliminary testsSubjects: Machine Learning (cs.LG); Dynamical Systems (math.DS); Chaotic Dynamics (nlin.CD)
Training neural networks involves optimizing parameters to minimize a loss function, where the nature of the loss function and the optimization strategy are crucial for effective training. Hyperparameter choices, such as the learning rate in gradient descent (GD), significantly affect the success and speed of convergence. Recent studies indicate that the boundary between bounded and divergent hyperparameters can be fractal, complicating reliable hyperparameter selection. However, the nature of this fractal boundary and methods to avoid it remain unclear. In this study, we focus on GD to investigate the loss landscape properties that might lead to fractal trainability boundaries. We discovered that fractal boundaries can emerge from simple nonconvex perturbations, i.e., adding or multiplying cosine type perturbations to quadratic functions. The observed fractal dimensions are influenced by factors like parameter dimension, type of nonconvexity, perturbation wavelength, and perturbation amplitude. Our analysis identifies "roughness of perturbation", which measures the gradient's sensitivity to parameter changes, as the factor controlling fractal dimensions of trainability boundaries. We observed a clear transition from nonfractal to fractal trainability boundaries as roughness increases, with the critical roughness causing the perturbed loss function nonconvex. Thus, we conclude that fractal trainability boundaries can arise from very simple nonconvexity. We anticipate that our findings will enhance the understanding of complex behaviors during neural network training, leading to more consistent and predictable training strategies.
 [19] arXiv:2406.13995 (crosslist from stat.ML) [pdf, html, other]

Title: Prediction of Unobserved Bifurcation by Unsupervised Extraction of Slowly TimeVarying System Parameter Dynamics from Time Series Using Reservoir ComputingComments: 17 pages, 7 figuresSubjects: Machine Learning (stat.ML); Machine Learning (cs.LG); Chaotic Dynamics (nlin.CD)
Nonlinear and nonstationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to learn and predict such systems from observed time series data. However, predicting the behavior of systems with temporal parameter variations without knowledge of true parameter values remains a significant challenge. This study leverages the reservoir computing framework to address this problem by unsupervised extraction of slowly varying system parameters from time series data. We propose a model architecture consisting of a slow reservoir with long timescale internal dynamics and a fast reservoir with short timescale dynamics. The slow reservoir extracts the temporal variation of system parameters, which are then used to predict unknown bifurcations in the fast dynamics. Through experiments using data generated from chaotic dynamical systems, we demonstrate the ability to predict bifurcations not present in the training data. Our approach shows potential for applications in fields such as neuroscience, material science, and weather prediction, where slow dynamics influencing qualitative changes are often unobservable.
 [20] arXiv:2406.14350 (crosslist from physics.bioph) [pdf, html, other]

Title: A firstprinciples geometric model for dynamics of motordriven centrosomal astersComments: 50 pages (doublespaced), eight figures in main text, and four figures in the supplemental materialSubjects: Biological Physics (physics.bioph); Adaptation and SelfOrganizing Systems (nlin.AO); Subcellular Processes (qbio.SC)
The centrosomal aster is a mobile cellular organelle that exerts and transmits forces necessary for nuclear migration and spindle positioning. Recent experimental and theoretical studies of nematode and human cells demonstrate that pulling forces on asters by cortical force generators are dominant during such processes. We present a comprehensive investigation of a firstprinciples model of aster dynamics, the Smodel (S for stoichiometry), based solely on such forces. The model evolves the astral centrosome position, a probability field of cellsurface motor occupancy by centrosomal microtubules (under an assumption of stoichiometric binding), and free boundaries of unattached, growing microtubules. We show how cell shape affects the centering stability of the aster, and its transition to oscillations with increasing motor number. Seeking to understand observations in singlecell nematode embryos, we use accurate simulations to examine the nonlinear structures of the bifurcations, and demonstrate the importance of binding domain overlap to interpreting genetic perturbation experiments. We find a rich dynamical landscape, dependent upon cell shape, such as internal equatorial orbits of asters that can be seen as traveling wave solutions. Finally, we study the interactions of multiple asters and demonstrate an effective mutual repulsion due to their competition for cortical force generators. We find, amazingly, that asters can relax onto the vertices of platonic and nonplatonic solids, closely mirroring the results of the classical Thomson problem for energyminimizing configurations of electrons constrained to a sphere and interacting via repulsive Coulomb potentials. Our findings both explain experimental observations, providing insights into the mechanisms governing spindle positioning and cell division dynamics, and show the possibility of new nonlinear phenomena in cell biology.
Cross submissions for Friday, 21 June 2024 (showing 14 of 14 entries )
 [21] arXiv:2201.09812 (replaced) [pdf, html, other]

Title: Natural Selection and Random Matrix TheorySubjects: Chaotic Dynamics (nlin.CD); Populations and Evolution (qbio.PE)
We will study the relationship between two wellknown theories, genetic evolution and random matrix theory in the context of manybody systems. We show that the time evolution of certain quantum mechanical toy models is similar to that of a living cell. It is also suggested that genetic evolution can be described by a random matrix theory with statistical distribution in which natural selection acts as a GrossWittenWadia phase transition.
 [22] arXiv:2402.08634 (replaced) [pdf, html, other]

Title: Coexistence of uniform and oscillatory states resulting from nonreciprocity and conservation lawsSubjects: Pattern Formation and Solitons (nlin.PS); Soft Condensed Matter (condmat.soft)
Employing a twospecies CahnHilliard model with nonreciprocal interactions we show that the interplay of nonreciprocity and conservation laws results in the coexistence of uniform stationary and oscillatory phases as well as of uniform and crystalline phases. For nonequilibrium models with a \textit{spurious gradient dynamics structure} [T. FrohoffH{ü}lsmann \textit{et al.}, Phys.\ Rev.\ E 107, 64210 (2023)] the coexistence between nonequilibrium phases can nevertheless be predicted by a Maxwell doubletangent construction including phases with sustained outofequilibrium dynamics. This is further corroborated by bifurcation studies and time simulations.
 [23] arXiv:2404.02998 (replaced) [pdf, html, other]

Title: Dispersive shock waves in a onedimensional dropletbearing environmentSathyanarayanan Chandramouli, Simeon I. Mistakidis, Garyfallia C. Katsimiga, Panayotis G. KevrekidisComments: 15 pages, 9 figuresSubjects: Pattern Formation and Solitons (nlin.PS); Quantum Physics (quantph)
We demonstrate the controllable generation of distinct types of dispersive shockwaves emerging in a quantum droplet bearing environment with the aid of steplike initial conditions. Dispersive regularization of the ensuing hydrodynamic singularities occurs due to the competition between meanfield repulsion and attractive quantum fluctuations. This interplay delineates the dominance of defocusing (hyperbolic) and focusing (elliptic) hydrodynamic phenomena respectively being designated by real and imaginary speed of sound. Specifically, the symmetries of the extended GrossPitaevskii model lead to a threeparameter family, encompassing two densities and a relative velocity, of the underlying Riemann problem utilized herein. Surprisingly, dispersive shock waves persist across the hyperbolictoelliptic threshold, while a plethora of additional wave patterns arise, such as rarefaction waves, traveling dispersive shock waves, (anti)kinks and droplet wavetrains. The classification and characterization of these features is achieved by deploying Whitham modulation theory. Our results pave the way for unveiling a multitude of unexplored coherently propagating waveforms in such attractively interacting mixtures and should be detectable by current experiments.
 [24] arXiv:2405.08414 (replaced) [pdf, html, other]

Title: ICO learning as a measure of transient chaos in PTsymmetric Li\'enard systemsComments: 9 pages, 12 figuresSubjects: Adaptation and SelfOrganizing Systems (nlin.AO); Chaotic Dynamics (nlin.CD); Computational Physics (physics.compph)
In this article, we investigate the implications of the unsupervised learning rule known as InputCorrelations (ICO) learning in the nonlinear dynamics of two linearly coupled PTsymmetric Liénard oscillators. The fixed points of the oscillator have been evaluated analytically and the Jacobian linearization is employed to study their stability. We find that on increasing the amplitude of the external periodic drive, the system exhibits perioddoubling cascade to chaos within a specific parametric regime wherein we observe emergent chaotic dynamics. We further notice that the system indicates an intermittency route to chaos in the chaotic regime. Finally, in the period4 regime of our bifurcation analysis, we predict the emergence of transient chaos which eventually settles down to a period2 oscillator response which has been further validated by both the maximal FiniteTime Lyapunov Exponent (FTLE) using the wellknown GramSchmidt orthogonalization technique and the Hilbert Transform of the timeseries. In the transiently chaotic regime, we deploy the ICO learning to analyze the timeseries from which we identify that when the chaotic evolution transforms into periodic dynamics, the synaptic weight associated with the timeseries of the loss oscillator exhibits stationary temporal evolution. This signifies that in the periodic regime, there is no overlap between the filtered signals obtained from the timeseries of the coupled PTsymmetric oscillators. In addition, the temporal evolution of the weight associated with the stimulus mimics the behaviour of the Hilbert transform of the timeseries.
 [25] arXiv:2309.14645 (replaced) [pdf, html, other]

Title: A nonparametric learning framework for nonlinear robust output regulationComments: 17 pages; Nonlinear control; iISS stability; output regulation; parameter estimation; Nonadaptive controlSubjects: Systems and Control (eess.SY); Optimization and Control (math.OC); Adaptation and SelfOrganizing Systems (nlin.AO)
A nonparametric learning solution framework is proposed for the global nonlinear robust output regulation problem. We first extend the assumption that the steadystate generator is linear in the exogenous signal to the more relaxed assumption that it is polynomial in the exogenous signal. Additionally, a nonparametric learning framework is proposed to eliminate the construction of an explicit regressor, as required in the adaptive method, which can potentially simplify the implementation and reduce the computational complexity of existing methods. With the help of the proposed framework, the robust nonlinear output regulation problem can be converted into a robust nonadaptive stabilization problem for the augmented system with integral inputtostate stable (iISS) inverse dynamics. Moreover, a dynamic gain approach can adaptively raise the gain to a sufficiently large constant to achieve stabilization without requiring any a priori knowledge of the uncertainties appearing in the dynamics of the exosystem and the system. Furthermore, we apply the nonparametric learning framework to globally reconstruct and estimate multiple sinusoidal signals with unknown frequencies without the need for adaptive parametric techniques. An explicit nonlinear mapping can directly provide the estimated parameters, which will exponentially converge to the unknown frequencies. Finally, a feedforward control design is proposed to solve the linear output regulation problem using the nonparametric learning framework. Two simulation examples are provided to illustrate the effectiveness of the theoretical results.
 [26] arXiv:2310.12624 (replaced) [pdf, html, other]

Title: Poles, Shocks and Tygers: The Timereversible Burgers equationComments: 25 pages, 18 figuresSubjects: Fluid Dynamics (physics.fludyn); Statistical Mechanics (condmat.statmech); Chaotic Dynamics (nlin.CD)
We construct a formally timereversible, onedimensional forced Burgers equation by imposing a global constraint of energy conservation, wherein the constant viscosity is modified to a fluctuating statedependent dissipation coefficient. The system exhibits dynamical properties which bear strong similarities with those observed for the Burgers equation and can be understood using the dynamics of the poles, shocks, and truncation effects, such as tygers. A complex interplay of these give rise to interesting statistical regimes ranging from hydrodynamic behavior to a completely thermalized warm phase. The end of the hydrodynamic regime is associated with the appearance of a shock in the solution and a continuous transition leading to a truncationdependent state. Beyond this, the truncation effects such as tygers and the appearance of secondary discontinuity at the resonance point in the solution strongly influence the statistical properties. These disappear at the second transition, at which the global quantities exhibit a jump and attain values that are consistent with the establishment of a quasiequilibrium state characterized by energy equipartition among the Fourier modes. Our comparative analysis shows that the macroscopic statistical properties of the formally timereversible system and the Burgers equation are equivalent in all the regimes, irrespective of the truncation effects, and this equivalence is not just limited to the hydrodynamic regime, thereby further strengthening the Gallavotti's equivalence conjecture. The properties of the system are further examined by inspecting the complex space singularities in the velocity field of the Burgers equation. Furthermore, an effective theory is proposed to describe the discontinuous transition.
 [27] arXiv:2402.11463 (replaced) [pdf, html, other]

Title: Attractor Memory for LongTerm Time Series Forecasting: A Chaos PerspectiveComments: arXiv admin note: text overlap with arXiv:nlin/0307015 by other authorsSubjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Chaotic Dynamics (nlin.CD)
In longterm time series forecasting (LTSF) tasks, an increasing number of models have acknowledged that discrete time series originate from continuous dynamic systems and have attempted to model their dynamical structures. Recognizing the chaotic nature of realworld data, our model, \textbf{\textit{Attraos}}, incorporates chaos theory into LTSF, perceiving realworld time series as observations from unknown highdimensional chaotic dynamic systems. Under the concept of attractor invariance, Attraos utilizes nonparametric Phase Space Reconstruction embedding and the proposed multiscale dynamic memory unit to memorize historical dynamics structure and predicts by a frequencyenhanced local evolution strategy. Detailed theoretical analysis and abundant empirical evidence consistently show that Attraos outperforms various LTSF methods on mainstream LTSF datasets and chaotic datasets with only onetwelfth of the parameters compared to PatchTST.
 [28] arXiv:2405.09945 (replaced) [pdf, html, other]

Title: Nearhorizon chaos beyond Einstein gravityComments: 21 pages, 63 figures, 1 tableSubjects: General Relativity and Quantum Cosmology (grqc); High Energy Physics  Theory (hepth); Chaotic Dynamics (nlin.CD)
We investigate chaos in the dynamics of outgoing massless particles near the horizon of static spherically symmetric (SSS) black holes in two wellmotivated models of $f(R)$ gravity. In both these models, we probe chaos in the particle trajectories (under suitable harmonic confinement) in the vicinity of the black hole horizons, for a set of initial conditions. The particle trajectories, associated Poincar$\acute{e}$ sections, and Lyapunov exponents clearly illustrate the role played by the black hole horizon in the growth of chaos. We find that with increasing energy, the particle trajectories explore regions closer to the black hole horizon, with reduced overlap between two initially close trajectories. We demonstrate how this energy range is controlled by the parameters of the modified gravity theory under consideration. The growth of chaos in such a classical setting is known to respect a surface gravity bound arising from universal aspects of particle dynamics close to the black hole horizon [K. Hashimoto and N. Tanahashi, Phys. Rev. D 95, 024007 (2017)], analogous to the quantum MSS bound [J. Maldacena, S.H. Shenker and D. Stanford, JHEP 08 (2016) 106]. Interestingly, both models studied in our work respect the bound, in contrast to some of the other models of $f(R)$ gravity in the existing literature. The work serves as a motivation to use chaos as an additional tool to probe Einstein gravity in the strong gravity regime in the vicinity of black hole horizons.