Mathematical Sciences: Lyapunov Exponents and Stable Manifolds for Stochastic Delay Systems

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The principal investigator will continue to work on developing a theory of Lyapunov exponents and stable manifolds for stochastic dynamical systems with finite memory. Such dynamical systems occur in many applied sciences as models of physical phenomena incorporating the past history of the state variables as well as the effects of random fluctuations or noise. One example would be a hydrodynamic model of blood circulation while a second would be a model for population growth. Small random perturbations of deterministic delay models also lead very naturally to stochastic differential delay systems. This research will lead to discoveries concerning the almost sure dynamics of these models.