Related papers: Collective Behavior of Coupled Chaotic Maps
Dynamics of coupled chaotic oscillators on a network are studied using coupled maps. Within a broad range of parameter values representing the coupling strength or the degree of elements, the system repeats formation and split of coherent…
We study two-dimensional chaotic standard maps coupled along the edges of scale-free trees and tree-like subgraph (4-star) with a non-symplectic coupling and time delay between the nodes. Apart from the chaotic and regular 2-periodic…
Chaotic evolution of structures in Coupled map lattice driven by identical noise on each site is studied (a structure is a group of neighbouring lattice-sites for whom values of dynamical variable follow certain predefined pattern). Number…
The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the…
Coupled map lattices are a paradigm of higher-dimensional dynamical systems exhibiting spatio-temporal chaos. A special case of non-hyperbolic maps are one-dimensional map lattices of coupled Chebyshev maps with periodic boundary…
Networks of chaotic units with static couplings can synchronize to a common chaotic trajectory. The effect of dynamic adaptive couplings on the cooperative behavior of chaotic networks is investigated. The couplings adjust to the activities…
We study how periodicity manifestations recently found in the turbulent globall coupled maps depend on the global feature of the couplings. We examine three non-locally coupled map models. In the first two, the all-to-all interaction is…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…
It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the…
We propose and study a local map capable of describing the full variety of dynamical states, ranging from regular to chaotic, obtained when a nematic liquid crystal is subjected to a steady shear flow. The map is formulated in terms of a…
We study the dynamics of one--dimensional discrete models of one--component active medium built up of spatially inhomogeneous chains of diffusively coupled piecewise linear maps. The nonhomogeneities (``defects'') are treated in terms of…
The effect of the chaotic dynamical states of the agents on the coevolution of cooperation and synchronization in a structured population of the agents remains unexplored. With a view to gaining insights into this problem, we construct a…
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…
The dynamics of globally coupled map lattices can be described in terms of a nonlinear Frobenius--Perron equation in the limit of large system size. This approach allows for an analytical computation of stationary states and their…
We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to…
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…
We consider a model in which a collective state couples to a large number of background states. The background states can be chosen to have properties which are classically characterized as regular or chaotic. We found that the dynamical…
The behavior of two-dimensional coupled map lattices is studied with respect to the global stabilization of unstable local fixed points without external control. It is numerically shown under which circumstances such inherent global…
Coupled map lattices have been widely used as models in several fields of physics, such as chaotic strings, turbulence, and phase transitions, as well as in other disciplines, such as biology (ecology, evolution) and information processing.…
We show that the dynamical behavior of a coupled map lattice where the individual maps are Bernoulli shift maps can be solved analytically for integer couplings. We calculate the invariant density of the system and show that it displays a…