Global stability for a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge

• Main Authors: Yantao Luo, Long Zhang, Zhidong Teng, Tingting Zheng
• Format: Article
• Language: English
• Published: SpringerOpen 2020-03-01
• Series: Advances in Difference Equations
• Subjects: Nonautonomous; Reaction-diffusion; Modified Leslie–Gower; Predator-prey; Global asymptotic stability
• Online Access: http://link.springer.com/article/10.1186/s13662-020-02563-7

Abstract In this paper, a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge is proposed. Applying the comparison theory of differential equation, sufficient average criteria on the permanence of solutions and the existence of the positive periodic solutions are established. Moreover, the existence region of the positive periodic solutions is an invariant region dependent on t. Then, constructing a suitable Lyapunov function, we obtain sufficient conditions to guarantee the global asymptotic stability of the positive periodic solutions. Finally, we do some numerical simulations to verify our main results and investigate the effect of prey refuge on the dynamics of the system.