Mathematical Sciences: Nonlinear Dynamical Systems

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This project will study qualitative properties of nonlinear dynamical systems, with an emphasis on the following areas: (1) geometric theory of singularly perturbed differential equations, both finite and infinite dimensional; (2) differential delay equations arising in various areas (physiology, optics,biology) of science; and (3) dynamical systems exhibiting monotone and gradient-like behavior. In all these areas the focus will be on global structures such as attractors, periodic orbits, gradient structures and homo/heteroclinic orbits, and bifurcations of these structures.