相关论文: Non-transitive maps in phase synchronization

The nonlinear dynamics of a recently derived generalized Lorenz model (Macek and Strumik, Phys. Rev. E 82, 027301, 2010) of magnetoconvection is studied. A bifurcation diagram is constructed as a function of the Rayleigh number where…

We present a method based on symbolic dynamics for the detection of synchronization in networks of coupled maps and distinguishing between chaotic and random iterations. The symbolic dynamics are defined using special partitions of the…

We study synchronization of low-dimensional ($d=2,3,4$) chaotic piecewise linear maps. For Bernoulli maps we find Lyapunov exponents and locate the synchronization transition, that numerically is found to be discontinuous (despite…

We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…

The idea that chaos could be a useful tool for analyze nonlinear systems considered in this paper and for the first time the two time scale property of singularly perturbed systems is analyzed on chaotic attractor. The general idea…

We characterize the synchronization of an array of coupled chaotic elements as a phase transition where order parameters related to the joint probability at two sites obey power laws versus the mutual coupling strength; the phase transition…

We make a short review about the synchronization in coupled phase oscillator models. Next, we study the common-noise-induced synchronization among active rotators. At an intermediate noise strength, the noise-induced synchronization takes…

In this review we survey the literature on mean-field coupled maps. We start with the early works from the physics literature, arriving to some recent results from ergodic theory studying the thermodynamic limit of globally coupled maps and…

Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are…

A discontinuous area-preserving mapping derived from a sinusoidally-forced impacting system is studied. This system, the elastic impact oscillator, is very closely related to the accelerator models of particle physics such as the Fermi map.…

The influence of topological defects on phase synchronization and phase coherence in two-dimensional arrays of locally-coupled, nonidentical, chaotic oscillators is investigated. The motion of topological defects leads to a breakdown of…

The dynamics of two coupled piece-wise linear one-dimensional monostable maps is investigated. The single map is associated with Poincare section of the FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to the…

The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…

Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…

The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…

We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. As a result, the numerically…

In this paper we present an analytical study on the synchronization dynamics observed in unidirectionally-coupled quasiperiodically-forced systems that exhibit Strange Non-chaotic Attractors (SNA) in their dynamics. The SNA dynamics…

Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…

This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible…

The intermediate dynamics of composed one-dimensional maps is used to multiply attractors in phase space and create multiple independent bifurcation diagrams which can split apart. Results are shown for the composition of k-paradigmatic…