混沌动力学
In this article, we explore the possibility of a sub-harmonic $(1{:}2)$ entrainment and supercritical Hopf bifurcation in a van der Pol-Duffing oscillator that has been excited by two frequencies, comprising a slow parametric drive and a…
Gravitational and electromagnetic interactions are Hamiltonian systems with forces between pairs of particles. We propose an alternative: Hamiltonian dynamics with triplet interactions between point particles. Our system has a potential…
We perform time series analysis of small networks where every node is the slow-fast version of the denatured Morris--Lecar neuron proposed by Schaeffer and Cain. We choose popular coupling strategies from the literature and provide a…
We propose a method for training dynamical systems governed by Lagrangian mechanics using Equilibrium Propagation. Our approach extends Equilibrium Propagation - initially developed for energy-based models - to dynamical trajectories by…
A chain of harmonic oscillators with nonreciprocal coupling exhibits characteristic amplification behavior that serves as a classical analog of the non-Hermitian skin effect (NHSE). We extend this concept of nonreciprocal amplification to…
The processes that generate rogue waves on the sea surface remain a mystery. Despite their different natures, the nonlinear bending waves generated in a thin elastic plate share some similarities with waves on the surface of the sea. For…
Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. Here we show that learning from noise-free observations in such systems can be achieved up…
Traffic congestion, a daily frustration for millions and a multi-billion dollar drain on economies, has long resisted deep physical understanding. While simple theoretical models of traffic flow have suggested connections to critical…
This paper presents an operator-theoretic framework Linear Operator Causality Analysis (LOCA), for analysing causality in linearised dynamical systems, focusing here on fluid flows. We demonstrate that the matrix exponential of the…
Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the…
We study the dynamics of $N$-dimensional lattices of nonchaotic Rulkov neurons coupled with a flow of electrical current. We consider both nearest-neighbor and next-nearest-neighbor couplings, homogeneous and heterogeneous neurons, and…
This work proposes an innovative approach using machine learning to predict extreme events in time series of chaotic dynamical systems. The research focuses on the time series of the H\'enon map, a two-dimensional model known for its…
In this numerical study, recurrence quantification analysis of chaotic trajectories is explored to detect atypical dynamical behaviour in non-linear Hamiltonian systems. An ensemble of initial conditions is evolved up to a maximum iteration…
In this paper, we dealt the dynamic behavior of a magnetic structure, considering a shape memory spring and a non-ideal motor as excitation. It has fractal behavior of tits basins of attraction, for a set of parameters for energy…
The well known butterfly effect got its nomenclature from its two wings geometrical structure in phase space. There are chaotic dynamics from simple one-wing to multiple-wings complex structures in phase space. In this communication we…
We revisit a time-dependent, oval-shaped billiard to investigate a phase transition from bounded to unbounded energy growth. In the static case, the phase space exhibits a mixed structure. The chaotic sea in the static scenario leads to…
Nonlinear oscillations of a bubble carrying a constant charge and suspended in a fluid, undergoing periodic forcing due to incident ultrasound are studied. The system exhibits period-doubling route to chaos and the presence of charge has…
Machine learning (ML) is widely used to model chaotic systems. Among ML approaches, echo state networks (ESNs) have received considerable attention due to their simple construction and fast training. However, ESN performance is highly…
In this paper we study chaotic behavior in the forced dissipative non-linear Schr\"{o}dinger equation, so called the Bekki-Nozaki equation. Chaotic systems are often seen in a strong sensitivity to initial conditions,leading to error…
Digital implementations of chaotic systems often suffer from inherent degradation, limiting their long-term performance and statistical quality. To address this challenge, we propose a novel four-stage synchronized piecewise linear chaotic…