Gaussian processes, such as Brownian motion, have been widely used in modeling fluctuations, while some complex phenomena involve non-Gaussian Levy noise. Thus dynamical systems driven by non-Gaussian noise have attracted considerable attention recently. At certain ‘macroscopic’ level, non-Gaussianity of the noise manifests as nonlocality (or nonlocal operators in the Fokker-Planck equations).
The speaker presents recent work on escape probability, mean exit time, bifurcation and random invariant manifolds for non-Gaussian stochastic dynamical systems. The differences in dynamics under Gaussian and non-Gaussian noises are highlighted, theoretically or numerically.
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