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It included 8 participants and one observer. The goal of the group was to exchange ideas between two largely distinct aspects of differential systems driven by self-similar stochastic processes: the stochastic analysis angle and the theory of random dynamical systems. Each of the 9 people gave talks on various topics in each of these aspects. These talks… (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)
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 pseudo-stable and pseudo-unstable manifolds for a class of random partial differential equations and stochastic partial differential… (More)
In this paper, we study rotation numbers of random dynamical systems on the circle. We prove the existence of rotation numbers and the continuous dependence of rotation numbers on the systems. As an application, we prove a theorem on analytic conjugacy to a circle rotation.
of Talks In the multiple authors case, the name with * is the speaker. Abstract: (Preliminary report) We examine the asymptotic states of symmetric solutions to ∆u − grad W (u) = 0, u : R n → R n constructed by Alikakos and Fusco. Here W is equivariant under a finite reflection group and has n + 1 nondegenerate minima. Passing to the limit as x → ∞ in… (More)