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The focused research group on Stochastic Differential Equations driven by Fractional Brownian Motion as Random Dynamical Systems met from around 9:30am to around 5pm from Monday September 29 to Saturday October 4, 2008. It included 8 participants and one observer. The goal of the group was to exchange ideas between two largely distinct aspects of(More)
We consider a class of Cohen-Grossberg neural networks with delays. We prove the existence and global asymptotic stability of an equilibrium point and estimate the region of existence. Furthermore, we show that the trajectories of the neural networks with positive initial data will stay in the positive region if the amplification function satisfies a(More)
Annals of Probability 31(2003), 2109-2135. Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for stochastic ordinary differential equations is relatively mature. In this paper, we(More)
We prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behavior. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential(More)
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudostable and pseudo-unstable manifolds for a class of random partial differential equations and stochastic partial differential(More)