Leírás
Nonlinear dynamical systems are frequently influenced by random fluctuations. These fluctuations may be Gaussian or non-Gaussian, modeled respectively by Brownian motion or α-stable Lévy motion. The interplay between uncertainty and nonlinearity gives rise to rich and complex phenomena, including critical transitions between qualitatively distinct dynamical regimes. Such transitions—often referred to as tipping phenomena—are ubiquitous across science and engineering.
This interplay naturally leads to the study of nonlocal partial differential equations (PDEs), analyzed through linear and nonlinear Feynman–Kac formulas and local or nonlocal Kramers–Moyal expansions.
In this talk, the speaker will present recent advances in the theory of stochastic dynamical systems, with an emphasis on transition phenomena and their deep connections to deterministic and nonlocal PDEs.