We propose a new method to investigate collective behavior in a network of globally coupled chaotic elements generated by a tent map. In the limit of large system size, the dynamics is described with the nonlinear FrobeniusPerron equation. This equation can be transformed into a simple form by making use of the piecewise linear nature of the individual map. Our method is applied successfully to...

This work reports a systematic investigation of the distribution of periodic and aperiodic patternevolution in rings of diffusively coupled quadratic maps. Our main motivation here is the wish to investigate whether lattices of coupled maps can be effectively used to simulate a plethora of phenomena associated with climatic variability and change. Presently, simulations of these phenomena reduc...

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 the evolution of the single (or microscopic) elements of the system. The usual Lyapunov exponent is not able to capture the essential features of this macrosc...

In this work, an ensemble of economic interacting agents is considered. The agents are arranged in a linear array where only local couplings are allowed. The deterministic dynamics of each agent is given by a map. This map is expressed by two factors. The first one is a linear term that models the expansion of the agent’s economy and that is controlled by the growth capacity parameter. The seco...

Phase plots of coupled maps have shown turbulent, semi-ordered, intermittent and ordered behaviour as a function of control parameters for networks of uniform scale. We investigate the dependence of coupled map dynamics on scale, i.e. number of neurons. We compare results for globally coupled maps (GCMs) and ones with minor lesions, employing a new chaotic function that we propose. The behaviou...

We study the transition to coherence of an ensemble of globally coupled chaotic maps allowing for ensembles of nonidentical maps and for noise. The transition coupling strength is determined from a kind of transfer function of the perturbation evolution. We present analytical results, and we test these results using numerical experiments for several large systems consisting of ensembles of many...

We consider analytic coupled map lattices over Z with exponentially decaying interaction. We introduce Banach spaces for the infinite-dimensional system that include measures with analytic, exponentially bounded finite-dimensional marginals. Using residue calculus and ‘cluster expansion’-like techniques we define transfer operators on these Banach spaces. For these we get a unique probability m...

We study the critical behavior of period doubling in two coupled onedimensional maps with a single maximum of order z. In particurlar, the effect of the maximum-order z on the critical behavior associated with coupling is investigated by a renormalization method. There exist three fixed maps of the period-doubling renormalization operator. For a fixed map associated with the critical behavior a...

Coupled Tchebyscheff maps have recently been introduced to explain parameters in the standard model of particle physics, using the stochastic quantisation of Parisi and Wu. This paper studies dynamical properties of these maps, finding analytic expressions for a number of periodic states and determining their linear stability. Numerical evidence is given for nonlinear stability of some of these...

The effect of noise on a system of globally coupled chaotic maps is considered. Demographic stochasticity is studied since it provides both noise and a natural definition for extinction. A two-step model is presented, where the intrapatch chaotic dynamics is followed by a migration step with global dispersal. The addition of noise to the already chaotic system is shown to dramatically change it...