SINCRONIZAÇÃO E SUPRESSÃO DE CAOS EM REDES COM INTERAÇÃO DE LONGO ALCANCE

Abstract

Networks of coupled map are used as models to understand the spatiotemporal phenomena in spatially extended systems. In this work it is considered a network of coupled logistic maps in which the interaction among the elements decays according to a power law. In order to characterize the spatial distribution of the logistic map network state variables it was used diagnostic complex order parameter to quantify the synchronization of chaos. The synchronization and suppression of chaos were obtained in the parameter space through coupling values of the intensity and range of interaction among network elements. Others measures were calculated as the spectrum of Lyapunov, Lyapunov dimension and Kolmogorov-Sinai entropy. From the study of the coupled maps network, it was investigated the dynamics of a neuron network by means of collective behavior, and the synchronized state. Hindmarsh-Rose model is the model neuron chosen in this work, and it is described by a system of three first order differential equations coupled in the state variable that represents the membrane potential which shows a succession of alternating activity and rest state. The simulation allowed us to understand the case of a neuron Hindmarsh-Rose and its dynamic properties generation of pulses. The coupling case between two neurons in the master-slave configuration and synchronization in the network of neurons with non-local coupling were used in this work. The network of coupled logistic maps and the Hindmarsh-Rose neurons networks were investigated in the parameter spaces since the two networks constituents are different.