On the global asymptotic stability of a predator–prey model with Crowley–Martin function and stage structure for prey

Abstract

In this work, we present a mathematically rigorous analysis for the local and global asymptotic stability of a predator–prey model with Crowley–Martin function and stage structure for prey, which was proposed in a previous work [Applied Mathematics and Computation 232(2014) 810–819]. In the previous work, the local and global stability of the unique positive equilibrium point of this model were established under some sufficient conditions. Our objective is to re-establish the stability of this equilibrium point without these sufficient conditions. For this purpose, we propose a novel approach to show that the sufficient conditions proposed in the previous work are completely freed. More clearly, we use a well-known stability theorem of continuous-time nonlinear cascade systems and Lyapunov stability theorem to prove that the unique positive equilibrium point is asymptotically stable if it exists. Furthermore, the global stability of the boundary equilibrium point is also established based on the approach. Finally, some numerical simulations are performed to confirm the validity of the constructed theoretical results. The results indicate that there is a good agreement between the numerical simulations and theoretical results.