Caos booleano: em busca de sincronização

Abstract

The study of dynamical systems makes it possible to describe the characteristics of a infinity of phenomena, in particular, the study of nonlinear dynamical systems, which have stood out in the mathematical modeling scenario for presenting a rich behavior in dynamic informations and with several particularities. It is in this context that this work employs mathematical and computational tools based on concepts of analysis of nonlinear systems that are applied in the study of Lorenz system. Based on the analysis of phase plans, phase spaces, numerical simulations and the behaviors that such a system presents, we will analyze the dynamics of Autonomous Boolean Networks, in which the future state of the network will be determined by the history of switching events, previous interactions and delays along the links. As well as we will analyze the study of the non-ideal behavior of logic gates, the rejection of short pulses and an analysis of the memory effect called "degradation" play a fundamental role in understanding the dynamics and chaos presented by the network under discussion. Therefore, the knowledge of the factors that can generate chaotic behavior in Autonomous Boolean Networks with time delays will allow the study of synchronization between Autonomous Boolean Networks.