Nonlinear dynamics

Abstract

One of the goals of this project is to promote the integration of the groups Controle de Oscilações (CO)/Departamento de Física Aplicada and the Laboratório de Fenômenos Não-Lineares (LFNL)/Departamento de Física Geral, that have developed research in nonlinear dynamical systems. As the interaction between the researchers and students of both groups has been intense and positive (one article in cooperation was published in Physical Review E 58,4009-4011 September/1998) the integration of both groups in a common long term project will allow them to become more efficient and competitive. Controle de Oscilações (CO), this group will study the control of oscillations produced by instabilities and turbulence that limits and deteriorates the magnetic confinement of plasma in tokamaks. In this investigation will be used the usual methods of dynamical systems analysis and turbulence in fluids. To control the dissipative dynamical systems it will be investigated the actions of external perturbations, periodically continuous or pulsed, as well as the effects of small variations of the control parameter that changes qualitatively the analyzed trajectories. It will also be investigated the appearance, the structure and the control of turbulence in fluids and plasmas; the reconnecting of the magnetic field lines; the diffusion in multidimensional systems; the non-normal analysis in tokamaks; chaos in the space of parameters. It will also be studied chaos in lasers, in mechanical systems and the control of biological cycles. Laboratório de Fenômenos Não-Lineares (LFNL) the aim of the laboratory is the experimental studies of nonlinear dynamical systems. The first experiment was assembled to study the dynamics of the water drop formation in the leaky faucet and it is a paradigm of a system that presents chaotic behavior. One characteristic of the lab is the development of low cost equipment. Three new experiments are being developed: a) the study of the formation dynamics of air bubble in viscous fluids; b) the study of oscillations in flames, and c) to study granular systems. We have been characterized the dynamical systems by using topological analysis and symbolic dynamics as well as by using metric characterization such as the calculation of the highest Lyapunov exponent, embedded dimension, etc. Both groups together intend to study: the chaos control in electronic circuits and in the drop and bubble formation; chaos in communications; the space of parameters in the leaky faucet; and to consolidate the collaboration in the characterization of dynamical systems. We also intend to strengthen the cooperation with other groups as the ones in UFRGS, UFPR and UFF; and with in São Paulo state as the ones in ICB-USP, Escola Politécnica-USP, Museu de Zoologia-USP, UNESP (Rio Claro and Guaratinguetá), and INPE-São José dos Campos. (AU)