Colloquium Jan. 6, 3-4pm NS 212C
Speaker : Dr. Dang Nguyen, University of Alabama
Date: January 6, 2020 (Monday)
Time: 3:00 – 4:00 pm
Room: NS 212C
Title: Persistence and Extinction of Stochastic Kolmogorov Systems.
In recent years there has been a growing interest in the study of the dynamics of stochastic populations. A key question in population biology is to understand the conditions under which populations coexist or go extinct. Theoretical and empirical studies have shown that coexistence can be facilitated or negated by both biotic interactions and environmental fluctuations. We study the dynamics of n populations that live in a stochastic environment and which can interact nonlinearly (through competition for resources, predator-prey behavior, etc.). The environmental variation is modeled by white noise and/or color noise. We give sharp conditions under which the populations converge exponentially fast to their unique stationary distribution as well as conditions under which some populations go extinct exponentially fast. Examples are also given to illustrate how stochasticity can facilitate or inhibit persistence of populations.