Mathematical Sciences Colloquium presents Dr. Hai Dang Nguyen

Friday, November 13, 2020 The event started -1231 days ago

3:00 PM 4:00 PM

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UNIVERSITY OF ALABAMA IN HUNTSVILLE MATHEMATICAL SCIENCES COLLOQUIUM

Dr. Hai Dang Nguyen
Department of Mathematics
University of Alabama Tuscaloosa

Persistence and Extinction of Some Stochastic Kolmogorov Systems

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.

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Conference/Lecture
department
College of Science, Department of Mathematical Sciences
Audience
Public, Students, Faculty and Staff, Alumni

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