Ni, Wenjie

Shi, Junping

Wang, Mingxin

2020-08

<p>A diffusive Lotka-Volterra competition model is considered and the combined effect of spatial dispersal and spatial variations of resource on the population persistence and exclusion is studied. A new Lyapunov functional method and a new integral inequality are developed to prove the global stability of non-constant equilibrium solutions in heterogeneous environment. The general result is applied to show that in a two-species system in which the diffusion coefficients, resource functions and competition rates are all spatially heterogeneous, the positive equilibrium solution is globally asymptotically stable when it exists, and it can also be applied to the system with arbitrary number of species under the assumption of spatially heterogeneous resource distribution, for which the monotone dynamical system theory is not applicable.</p>

Calculus of Variations and Partial Differential Equations, 59(4), p. 1-28

1432-0835

0944-2669

https://hdl.handle.net/1959.11/31885

Springer

Global stability of nonhomogeneous equilibrium solution for the diffusive Lotka-Volterra competition model

Journal Article

Publication