Mathematical Sciences: Dynamics of Nonlinear Models in Biology and Chemistry; Wave Solutions of Parabolic Differential Equations

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This proposal is to continue research in several areas of nonlinear applied dynamics. Excitable systems---systems which can be triggered by a small stimulus---arise as models of several physiological and chemical phenomena. It is proposed to study such systems, with an emphasis on understanding the periodic and aperiodic behavior that is seen. Another project is studying models of polymerization reactors with multiple initiators, in collaboration with some chemical engineers. The emphasis is to model industrial processes as completely as possible and understand behaviors of reactors under different operating conditions so as to effect control, and in particular, prevent catastrophic runaway of reactors. It is also proposed to continue work on understanding the stability of standing-and travelling-wave solutions of parabolic differential equations.