含有猎物避难所和恐惧效应的反应扩散捕食者-食饵模型的动力学

Dynamics of a reaction-diffusion predator-prey model incorporating prey refuge and fear effect

针对具有猎物避难所和恐惧效应的反应扩散捕食者-食饵系统,研究系统正常数解的图灵不稳和系统解的先验估计,并证明在一定的参数条件下系统非常数正稳态解的不存在性。此外,以捕食者的扩散系数为分歧参数,构建分歧解的全局结构,得到当捕食者的扩散系数大于某个临界值时,分歧解可以延拓到无穷。最后,通过数值模拟验证并补充理论结果。

For a reaction-diffusion predator-prey system with prey refuge and fear effect,the Turing instability of the positive constant solution for the system and a priori estimates of solutions for the system are investigated.It is proved that there is no nonconstant positive steady-state solution for the system under certain parameter conditions.Moreover,taking the diffusion coefficient of the predator as the bifurcation parameter,the global structure of the bifurcation solution is constructed.It is found that the bifurcation solution can be extended to infinity when the diffusion coefficient of predator is greater than some critical value.Finally,by numerical simulations,the theoretical results are verified and supplemented.