Mathematics | |
Turing Instability and Spatiotemporal Pattern Formation Induced by Nonlinear Reaction Cross-Diffusion in a Predator–Prey System with Allee Effect | |
Yangyang Shao1  Xinyue Xu1  Yan Meng1  | |
[1] School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China; | |
关键词: cross-diffusion; Allee effect; Turing instability; pattern formation; numerical simulation; | |
DOI : 10.3390/math10091500 | |
来源: DOAJ |
【 摘 要 】
The Allee effect is widespread among endangered plants and animals in ecosystems, suggesting that a minimum population density or size is necessary for population survival. This paper investigates the stability and pattern formation of a predator–prey model with nonlinear reactive cross-diffusion under Neumann boundary conditions, which introduces the Allee effect. Firstly, the ODE system is asymptotically stable for its positive equilibrium solution. In a reaction system with self-diffusion, the Allee effect can destabilize the system. Then, in a reaction system with cross-diffusion, through a linear stability analysis, the cross-diffusion coefficient is used as a bifurcation parameter, and instability conditions driven by the cross-diffusion are obtained. Furthermore, we show that the system (5) has at least one inhomogeneous stationary solution. Finally, our theoretical results are illustrated with numerical simulations.
【 授权许可】
Unknown