U.S.-Japan Cooperative Research: Topological and Singular Perturbation Methods with Applications to Nonlinear Differential Equations

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9315117 Mischaikow This awards supports a two-year cooperative research project between Professor Konstantin Mischaikow, Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, and Professor Yasumasa Nishiura, Department of Mathematics, Hiroshima University, Hiroshima, Japan. The objective of the project is to develop theoretical techniques for use in dynamical systems by integrating analytical and topological methods, and then to apply them to several problems arising from systems of reaction diffusion equations. Two other Japanese researchers -- Hiroshi Kokubu of Kyoto University and Hiroe Oka of Ryukoku University -- will also participate in the project. During his visits to Japan, Professor Mischaikow will attempt to combine two viewpoints of dynamics and bifurcation theory: an algebraic-topologic approach, based primarily on the Conley index, which is his expertise, and an analytic approach based on singular perturbation theory represented by the three Japanese researchers. The long-range goal of the project is to use the information to understand the appearance of complicated, possibly chaotic, dynamics in specified dynamical systems generated by partial differential equations. Some prototype models, new approaches, and preliminary results have already been achieved through prior collaboration of the U.S. and Japanese research groups. ***