混沌动力学
We numerically investigate the orbital dynamics of a two-dimensional galactic model, emphasizing the influence of stable and unstable manifolds on the evolution of orbits. In our analysis we use evaluations of the system's Lagrangian…
Billiard models of single particles moving freely in two-dimensional regions enclosed by hard walls, have long provided ideal toy models for the investigation of dynamical systems and chaos. Recently, billiards with (semi-)permeable walls…
Disorder is often seen as detrimental to collective dynamics, yet recent work has shown that heterogeneity can enhance network synchronization. However, its constructive role in stabilizing nontrivial cooperative patterns remains largely…
Evolutionary changes impacts interactions among populations and can disrupt ecosystems by driving extinctions or by collapsing population oscillations, posing significant challenges to biodiversity conservation. This study addresses the…
Network resilience, dynamically quantified by the Fiedler value (\(\lambda_2\),the second smallest eigenvalue of the Laplacian matrix) ensures functional stability and efficient energy transmission, yet also introduces vulnerabilities that…
Cardiac models are examples of excitable systems and can support stable spiral waves. For certain parameter values, however, these spiral waves can become unstable, resulting in spiral defect chaos (SDC), characterized by the continuous…
We will study the relationship between two well-known theories, genetic evolution and random matrix theory in the context of many-body systems. It is suggested that genetic evolution can be described by a random matrix theory with…
We use the theory of spectral submanifolds (SSMs) to develop a low-dimensional reduced-order model for plane Couette flow in the permanently chaotic regime studied by Kreilos & Eckhardt (2012). Our three-dimensional model is obtained by…
We reveal the symplectic nature of parameter-drift maps by embedding them into extended phase space. Applying the embedding to the parameter-drift standard nontwist map, our construction yields an autonomous symplectic map in extended phase…
In this review, we present a survey of the Lyapunov Error and Reversibility Error (\cite{Faranda2012}), and we propose a generalization to make them invariant to the choice of initial conditions. We first define a process as the evolution…
Two numerical methods are proposed for detection of coupling between multiple time series generated by deterministic nonlinear systems. The first detects interdependence or the existence of coupling between time series. The second…
This study investigates the interplay between a high-frequency external forcing and the intrinsic dynamics of a quantum nonlinear parametric oscillator. To analyze this system, classical equations of motion of the averages of quantum…
Some dynamical properties of nonlinear coupled systems can be described by the two-harmonic standard map, a two-dimensional area-preserving system with two parameters, where two distinct arbitrary resonant modes compete. Usually, the…
We propose an uncertainty principle for chaos, focusing on two key characteristics: alpha unpredictability and Lorenz sensitivity. This principle outlines a limitation on the relationship between two infinite sequences that underpin these…
The case of a star topology is studied on the example of Ikeda model-famous interdisciplinary system. The existence and stability conditions for the complete synchronization between constituent systems are found. An agreement between…
The Hurst effect in the signals describing ion channels' activity has been known for many years. This effect is present in the experimental recordings of single-channel currents, but not only. The sequences of dwell times of functionally…
We consider the problem of $n$ points with positive masses interacting pairwise with forces inversely proportional to the distance between them. In particular, it is the classical gravitational, Coulomb or photo-gravitational $n$-body…
We investigate the dynamics of a sliding top that is a rigid body with an ideal sharp tip moving in a perfectly smooth horizontal plane, so no friction forces act on the body. We prove that this system is integrable only in two cases…
Multifunctionality is ubiquitous in biological neurons. Several studies have translated the concept to artificial neural networks as well. Recently, multifunctionality in reservoir computing (RC) has gained the widespread attention of…
The bacteria metabolic process of open nonlinear dissipative system far from equilibrium point is modeled using classical methods of synergetics. The invariant measure and its convergence in the phase space of the system was obtained in…