Mathematical Sciences: Stochastic Hereditary Systems

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The investigator plans to develop a local stable manifold theory for non-linear stochastic hereditary systems with a bounded memory. A study of the Lyapunov spectrum near stationary hyperbolic orbits will be carried out. It is expected that the construction of the Lyapunov spectrum will lead to the existence of local stable manifolds around the stationary orbits. In specific case studies, the investigator hopes to obtain sharp estimates on the top Lyapunov exponent, and study its dependence on the noise variance and the delay. The proposer intends to analyze the behavior of dynamical systems that depend on chance and on the past history of their states. The proposed work sill examine the stability of such dynamical systems in the long term. The study will be supported by computer analysis of specific models from engineering and the physical sciences.