Abstract
Abstract In this paper, we consider a Beddington-DeAngelis predator-prey system with stage structure for predator and time delay incorporating prey refuge. By analyzing the characteristic equations, we study the local stability of the equilibrium of the system. Using the delay as a bifurcation parameter, the model undergoes a Hopf bifurcation at the coexistence equilibrium when the delay crosses some critical values. After that, by constructing a suitable Lyapunov functional, sufficient conditions are derived for the global stability of the system. Finally, the influence of prey refuge on densities of prey species and predator species is discussed.
Highlights
Predator-prey model is one of the basic models between di erent species in real world
By analyzing the characteristic equations, we study the local stability of the equilibrium of the system
Motivated by the works [21] and [28], a Beddington-DeAngelis predator-prey model with stage structure for predator and time delay incorporating prey refuge is investigated in this paper
Summary
Predator-prey model is one of the basic models between di erent species in real world. Wei and Fu [28] discussed the Hopf bifurcation and stability for predator-prey systems with Beddington-DeAngelis type functional response and stage structure for prey incorporating refuge x (t) = ax (t) − rx (t) − bx (t), x (t) = bx (t) − cx (t) − αx (t) − Motivated by the works [21] and [28], a Beddington-DeAngelis predator-prey model with stage structure for predator and time delay incorporating prey refuge is investigated in this paper.
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