Persistence and extinction of some stochastic Kolmogorov systems
Monday, June 4, 2018 - 3:00pm - 3:30pm
We consider asymptotic behaviors of some interacting populations in a fluctuating environment, which are described by Kolmogorov systems with white noise (stochastic differential equations) By analyzing the dynamics of the solution near the boundary and by determining Lyapunov exponents with respect to invariant probability measures on the boundary, we obtain conditions for both persistence and extinction of species. The conditions are sharp in the sense that only critical cases remain unsolved. We also estimate rates of convergence and have some comments on degenerate systems.