Related papers: Emergence of patterns in driven and in autonomous …
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 phenomenon of synchronization occurring in a locally coupled map lattice subject to an external drive is compared to the synchronization process in an autonomous coupled map system with similar local couplings plus a global interaction.…
We investigate the spatiotemporal dynamics of coupled circle map lattices, evolving under synchronous (parallel) updating on one hand and asynchronous (random) updating rules on the other. Synchronous evolution of extended spatiotemporal…
Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo…
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…
We present strong evidence that a coupled-map-lattice model for spatio-temporal intermittency belongs to the universality class of directed percolation when the updating rules are asynchronous, i.e. when only one randomly chosen site is…
We study the spatio-temporal behavior of simple coupled map lattices with periodic boundary conditions. The local dynamics is governed by two maps, namely, the sine circle map and the logistic map respectively. It is found that even though…
The pattern dynamics of the one-way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich. For medium and large coupling strengths, we find spatially periodic,…
A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity…
Dynamical coherent structure (pattern) formation in the Klein-Gordon lattice excited by periodic external field near the optical resonance is studied. It is shown that besides spatial patterns discovered recently (V.M.Burlakov,…
Studies of the phase diagram of the coupled sine circle map lattice have identified the presence of two distinct universality classes of spatiotemporal intermittency viz. spatiotemporal intermittency of the directed percolation class with a…
We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an…
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…
We consider the pattern formation problem in coupled identical systems after the global synchronized state becomes unstable. Based on analytical results relating the coupling strengths and the instability of each spatial mode (pattern) we…
A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states. As the value of a governing…
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…
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…
It is shown that the synchronization behavior of a system of chaotic maps subject to either an external forcing or a coupling function of their internal variables can be inferred from the behavior of a single element in the system, which…
By choosing a dynamical system with d different couplings, one can rearrange a system based on the graph with given vertex dependent on the dynamical system elements. The relation between the dynamical elements (coupling) is replaced by a…
Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results…