混沌动力学
A form of "remote synchronization" was recently described wherein amplitude fluctuations across a ring of non-identical, non-linear electronic oscillators become entrained into spatially-structured patterns. According to linear models and…
This paper addresses important control and observability aspects of the phase synchronization of two oscillators. To this aim a feedback control framework is proposed based on which issues related to master-slave synchronization are…
Collective modes of interacting many-body systems can be related to the motion on classically invariant manifolds. We introduce suitable coordinate systems. These coordinates are Cartesian in position and momentum space. They are collective…
In this article we provide the noncommutative Sprott models. We demonstrate, that effectively, each of them is described by system of three complex, ordinary and nonlinear differential equations. Apart of that, we find for such modified…
Trying to imagine three regions separated by a unique boundary seems a difficult task. However, this is exactly what happens in many dynamical systems showing Wada basins. Here, we present a new perspective on the Wada property: A Wada…
Time delays may cause dramatic changes to the dynamics of interacting oscillators. Coupled networks of interacting dynamical systems can behave unexpectedly when the signal between the vertices are time delayed. It has been shown for a very…
In this paper, we investigate numerically the stochastic ABC model, a toy model in the theory of astrophysical kinematic dynamos, within the recently proposed supersymmetric theory of stochastics (STS). STS characterises stochastic…
A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). For single particle systems with fully chaotic classical…
An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continu- ously coupled.…
The changeover from normal to super diffusion in time dependent billiards is explained analytically. The unlimited energy growth for an ensemble of bouncing particles in time dependent billiards is obtained by means of a two dimensional…
We propose to construct cross and joint ordinal pattern transition networks from multivariate time series for two coupled systems, where synchronizations are often present. In particular, we focus on phase synchronization, which is one of…
A suite of analytical and computational techniques based on symbolic representations of simple and complex dynamics, is further developed and employed to unravel the global organization of bi-parametric structures that underlie the…
Symmetry broken states arise naturally in oscillatory networks. In this Letter, we investigate chaotic attractors in an ensemble of four mean-coupled Stuart-Landau oscillators with two oscillators being synchronized. We report that these…
We provide a generic scheme to separate the particles of a mixture by their physical properties like mass, friction or size. The scheme employs a periodically shaken two dimensional dissipative lattice and hinges on a simultaneous transport…
We investigate the response of quasiperiodically driven nonlinear systems exhibiting strange non- chaotic attractors (SNAs) to deterministic input signals. We show that if one uses two square waves in aperiodic manner as input to a…
In turbulent Rayleigh-B\'enard convection one seeks the relationship between the heat transport, captured by the Nusselt number, and the temperature drop across the convecting layer, captured by Rayleigh number. In experiments, one measures…
This study uses the link between extreme value laws and dynamical systems theory to show that important dynamical quantities as the correlation dimension, the entropy and the Lyapunov exponents can be obtained by fitting observables…
It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependence on initial conditions (SDIC). Unfortunately, numerical noises (such as truncation error and round-off error)…
The purpose of this article is to review the developments related to the notion of local fractional derivative introduced in 1996. We consider its definition, properties, implications and possible applications. This involves the local…
This article discusses dependence on initial conditions in natural and social sciences with focus on physical science. The main focus is on the newly discovered rough dependence on initial data.