Global stability and pattern formation in a nonlocal diffusive Lotka–Volterra competition model |
| |
Authors: | Wenjie Ni Junping Shi Mingxin Wang |
| |
Institution: | 1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China;2. Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA |
| |
Abstract: | A diffusive Lotka–Volterra competition model with nonlocal intraspecific and interspecific competition between species is formulated and analyzed. The nonlocal competition strength is assumed to be determined by a diffusion kernel function to model the movement pattern of the biological species. It is shown that when there is no nonlocal intraspecific competition, the dynamics properties of nonlocal diffusive competition problem are similar to those of classical diffusive Lotka–Volterra competition model regardless of the strength of nonlocal interspecific competition. Global stability of nonnegative constant equilibria are proved using Lyapunov or upper–lower solution methods. On the other hand, strong nonlocal intraspecific competition increases the system spatiotemporal dynamic complexity. For the weak competition case, the nonlocal diffusive competition model may possess nonconstant positive equilibria for some suitably large nonlocal intraspecific competition coefficients. |
| |
Keywords: | 35K57 35K58 35K51 35B40 92D25 92D40 Diffusive Lotka–Volterra competition model Nonlocal interaction Global stability Non-constant equilibrium solution |
本文献已被 ScienceDirect 等数据库收录! |
|