Stability and traveling waves in a Beddington-DeAngelis type stage-structured predator-prey reaction-diffusion systems with nonlocal delays and harvesting

Abstract

The goal of this paper is to study the stability and traveling waves of stage-structured predator-prey reaction-diffusion systems of Beddington-DeAngelis functional response with both nonlocal delays and harvesting. By analyzing the corresponding characteristic equations, the local stability of various equilibria is discussed. We reduce the existence of traveling waves to the existence of a pair of upper-lower solutions by using the cross iteration method and the Schauder's fixed point theorem. The existence of traveling waves connecting the zero equilibrium and the positive equilibrium is then established by constructing a pair of upper-lower solutions. MSC: 35K57; 92D25

Periodic solution and its stability of a delayed Beddington‐DeAngelis type predator‐prey system with discontinuous control strategy

“…Many recent research work has focused on the BD model. () For example, Tripathi et al obtained the criteria for permanence, extinction, global stability of the interior equilibrium, and the existence of periodic orbits of the BD model . Zhang et al investigated the local and global stability of two steady states in a diffusive HBV model with delayed BD response .…”

“…Although the dynamical behaviors of a BD type predator‐prey system has been extensively investigated,() to the best of our knowledge, the delayed Beddington‐DeAngelis (BD) type predator‐prey system, especially under discontinuous control strategy, has been seldom considered. Moreover, owing to the characteristic of discontinuous control strategy, the results obtained for the system with optimal continuous harvesting policy, threshold policy, or weighted escapement policy cannot be directly applied to delayed BD type predator‐prey system with discontinuous control strategy.…”