Chaotic dynamics

Abstract

We propose an integrated program addressing fundamental aspects of the research in 'Chaotic Dynamics'. Our team is coordinated by Professor Celso Grebogi (Instituto de Física da USP) and consists of professors, researchers, post-doctoral fellows and students that belong to the following institutions: Instituto de Física da USP, Laboratório de Integração e Testes do INPE, Instituto de Ciências Matemática e de Computação da USP de São Carlos e Divisão de Ensino Fundamental do ITA. It is antecipated a strong participation of our collaborators in Brazil and abroad. The coordinator has recently joined the Universidade de São Paulo as Professor Titular after a 27 - year long academic career abroad. We also have a consensus for meaningful collaborations from many colleagues and former collaborators in Brasil and abroad. Our team possesses a unique expertise in alI aspects of the proposed research, including pioneers in the field who have made some of the basic contributions on which the proposed work is based. The goals in our proposed research include the development of basic theory, work on the theoretical implications of nonlinear dynamics in science and technology, and interactions with experimental researchers. In this context, the proposed research program addresses the following problem areas: (1) shadowing and deterministic modelling, (2) spatially-extended systems and the structure of parameter space, (3) active chaotic flows and complexity, (4) control, communication, and synchronization, (5) classical and quantum chaotic scattering, and (6) chaotic neural networks. (AU)