U.S.-Mexico Collaborative Research: Dynamics of Extended Systems and Coupled Map Lattices

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0104675LeviThis U.S. Mexico award will support Drs. Mark Levi, Howard Weiss, and Yakov Pesin in a research collaboration with Valentine Afraimovich of the Mathematics Department of the Unversidad Autonoma de San Luis de Potosi. The investigators plan to study: 1) Coupled map lattices corresponding to partial differential equations from physics and biology, in particular, the FitzHugh-Nagumo equation (which is of great interest in neurobiology). The collaborators intend to describe the ergodic properties of its local map and construct SRB measures for the attractor of this map. 2) The transition from coupled map lattices to partial differential equations via traveling waves, which will build a foundation for numerical modeling of some partial differential equations of evolution type. 3) The Dynamics of chains of coupled oscillators, in particular, those associated with the Sine-Gordon equation.A coupled map lattice is a discrete time dynamical system whose phase space is of a particular form, and for which the overall system exhibits translational symmetry.Coupled map lattices have recently gained wide popularity as models of spatio-temporal chaos and coherent structures. There is currently great interest in using coupled map lattices to model turbulence, nerve cells, phase transitions in statistical physics, and crystals. They also arise naturally from the discrete version of evolution partial differential equations.