Mathematical Biology Seminar Abstract
Jan 9, 2020
Junping Shi
William & Mary, Department of Mathematics
11:00 am in MSB 318 (Math Colloquium)

Global stability of the diffusive Lotka-Volterra competition model with stage structure or spatial heterogeneity

(i) The interactions between diffusion and spatial heterogeneity could create interesting dynamics for a spatial population model. We show that for two-component Lotka-Volterra competition model with spatially heterogeneous diffusion coefficients, intrinsic growth rates and competition rates, a spatially heterogeneous positive equilibrium solution is globally asymptotically stable when it exists. A similar result is also proved for multi-component Lotka-Volterra competition model with spatially heterogeneous intrinsic growth rates. We prove the result by using monotone dynamical theory, upper and lower solution methods, and a new Lyapunov functional method. This is a joint work with Wenjie Ni and Mingxin Wang. (ii) The global asymptotic behavior of the classical diffusive Lotka-Volterra competition model with stage structure is studied. A complete classification of the global dynamics is given for the weak competition case. It is shown that under otherwise same conditions, the species with shorter maturation time prevails. The method is also applied to the global dynamics of another delayed competition models. This is a joint work with Shanshan Chen.