Chaotic and stochastic dynamics in coupled map lattices

• Grant number: 05/04136-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: February 01, 2006
• End date: July 31, 2006
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Iberê Luiz Caldas
• Grantee: Sandro Ely de Souza Pinto
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this work we will study the dynamics of two coupled map lattices, namely: a lattice where the interactions between two maps take place following a power law of the distance between them; and a lattice with near- and nearest-neighbors and randomly distributed links. The dynamics of each elemental map will be governed by the logistic map, the baker map, and the tent map with scape. All studies will be done through the analyses of the Lyapunov spectrum, Lyapunov dimension, synchronization distance, synchronization time, and recurrence time. We will analyze the control parameter space for each coupled map lattice, with different individual dynamics and determine the synchronization, intermittency, chaotic, and chaos suppression regimes. The conditions for the transitions between those regimes and the associated phenomena will be studied. The spatio-temporal behavior will be studied through the observation of structures such as zigzags, kinks and antikinks. Through the study of the mean duration time of the laminar state of the intermittent regime and the recurrence time of that regime, we will analyze the statistical properties of this regime and compare them with the observed statistics at the emergence of turbulence in fluids and plasmas. (AU)