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TuesdayNov 14, 201711:15
Distinguished LecturerRoom 1
Speaker:Prof. Yakov PesinTitle:The Dynamical Systems Approach to Coupled Map LatticesAbstract:opens in new windowin html    pdfopens in new window
Coupled Map Lattices (CML) of an unbounded media appear as a result of time and space discretization of evolutional partial differential equations but can also be viewed as original phenomenological models of the medium. I will present the dynamical systems approach to study the global behavior of solutions of CML. In particular, I will describe the dynamics of the evolution operator on the set of traveling wave solutions of CML and discuss the phenomenon known as spatio-temporal chaos. I will illustrate this phenomenon in the particular example of CML associated with the famous FitzHue-Nagumo equation that describes propagation of voltage impulse through a nerve axon. When the leading parameter of this equation varies the dynamics undergoes several stages presenting Morse-Smale type dynamics, strange attractors and Smale horseshoes.