相关论文: Large Global Coupled Maps with Multiple Attractors

In this paper, we show the results of the strength of attractorruins for a globally coupled map. The globally coupled map (GCM) is a discrete dynamical system, and here we consider a model in which the logistic map is globally coupled. An…

Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…

In this paper we investigate how many periodic attractors maps in a small neighbourhood of a given map can have. For this purpose we develop new tools which help to make uniform cross-ratio distortion estimates in a neighbourhood of a map…

There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can…

A method to predict the emergence of different kinds of ordered collective behaviors in systems of globally coupled chaotic maps is proposed. The method is based on the analogy between globally coupled maps and a map subjected to an…

The attractors of a dynamical system govern its typical long-term behaviour. The presence of many attractors is significant as it means the behaviour is heavily dependent on the initial conditions. To understand how large numbers of…

The Globally Coupled Map Lattice (GCML) is one of the basic model of the intelligence activity. We report that, in its so-called turbulent regime, periodic windows of the element maps foliate and systematically control the dynamics of the…

We study a finite uni-directional array of "cascading" or "threshold coupled" chaotic maps. Such systems have been proposed for use in nonlinear computing and have been applied to classification problems in bioinformatics. We describe some…

The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…

In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to…

We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used, but they can give misleading results if used improperly and…

We study the attractor of Iterated Function Systems composed of infinitely many affine, homogeneous maps. In the special case of second generation IFS, defined herein, we conjecture that the attractor consists of a finite number of…

We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamical systems, as well as in systems modeling the dynamical…

In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…

We recently described a specific type of attractors of two-dimensional discontinuous piecewise linear maps, characterized by two discontinuity lines dividing the phase plane into three partitions, related to economic applications. To our…

We construct inducing schemes for general multi-dimensional piecewise expanding maps where the base transformation is Gibbs-Markov and the return times have exponential tails. Such structures are a crucial tool in proving statistical…

We revisit the globally coupled map lattice (GCML). We show that in the so called turbulent regime various periodic cluster attractor states are formed even though the coupling between the maps are very small relative to the non-linearity…

This article is devoted to a description of the dynamics of the phase flow of monotone contact Hamiltonian systems. Particular attention is paid to locating the maximal attractor (or repeller), which could be seen as the union of compact…

We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle…

We classify the measure theoretic attractors of general C^3 unimodal maps with quadratic critical points. The main ingredient is the decay of geometry.