| Abstract: |
| Dynamical systems arising in engineering and science are often subject to random fluctuations. The noisy fluctuations may be Gaussian or non-Gaussian, which are modeled by Brownian motion or $\alpha$-stable Levy motion, respectively. Non-Gaussianity of the noise manifests as nonlocality at a ``macroscopic level. Stochastic dynamical systems with non-Gaussian noise (modeled by $\alpha$-stable Levy motion) have attracted a lot of attention recently. The non-Gaussianity index $\alpha$ is a significant indicator for various dynamical behaviors.
The speaker will overview recent advances in geometrical methods for stochastic dynamical systems, including random invariant sets, random invariant manifolds, stochastic bifurcation, mean exit time, escape probability, tipping time, most probable orbits, and transition pathways between metastable states. |
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