Time：14:00-16:00, Tuesday, December 30 2025
Venue：E14-212
Speaker：Chenwan Zhou, New York University Shanghai
Title：Stochastic bifurcations of a three-dimensional stochastic Kolmogorov system
Abstract：In this paper we systematically investigate the stochastic bifurcations of both ergodic stationary measures and stochastic dynamics for a stochastic Kolmogorov differential system by the change of the sign of Lyapunov exponents. It is derived that there exists a threshold σ0 such that, if the noise intensity σ≥σ0, the noise destroys all bifurcations of the deterministic system and the corresponding stochastic Kolmogorov system is uniquely ergodic. On the other hand, when the noise intensity 0＜σ＜σ0 ,there exist further bifurcation thresholds such that the stochastic system undergoes bifurcations from the unique ergodic stationary measure to three different kinds of ergodic measures: (I) finitely many ergodic measures supported on rays, (II) infinitely many ergodic measures supported on rays, (III) infinitely many ergodic measures supported on invariant cones. Based on joint works with Prof. Dongmei Xiao and Prof. Deng Zhang.
