In this paper, we investigate a delayed predator–prey model with prey refuge where the predator population eats according to Beddington–DeAngelis type functional response. Firstly, consider existence of equilibrium points. By analyzing corresponding characteristic equations, local stability trivial equilibrium, predator–extinction balance, and coexistence system are discussed, Hopf bifurcations...

Recently, the population dynamic systems with impulsive controls have been researched by many authors. However, most of them are reluctant to study the seasonal effects on prey. Thus, in this paper, an impulsively controlled two-prey one-predator system with the Beddington-DeAngelis type functional response and seasonal effects is investigated. By using the Floquet theory, the sufficient condit...

We study the influence of the particular form of the functional response in two-dimensional predator-prey models with respect to the stability of the nontrivial equilibrium. This equilibrium is stable between its appearance at a transcritical bifurcation and its destabilization at a Hopf bifurcation, giving rise to periodic behavior. Based on local bifurcation analysis, we introduce a classific...

Abstract This article is concerned with the stationary problem for a prey-predator model prey-taxis/predator-taxis under homogeneous Dirichlet boundary conditions, where interaction governed by Beddington-DeAngelis functional response. We make detailed description of global bifurcation structure coexistence states and find ranges parameters which there exist states. At same time, some sufficien...

In the predator–prey system, predators can affect prey population by direct killing and predation fear. present study, we consider a delayed model with fear Beddington–DeAngelis functional response. The incorporates not only of predator on an intraspecific competition relationship, but also delay pregnancy delay. Apart from local stability analysis equilibrium points model, find that time chang...

Taking impulsive effects into account, an stochastic predator–prey system with the Beddington–DeAngelis functional response is proposed in this paper. First, transformed equivalent without pulses. Then, by constructing suitable functionals and applying extreme-value theory of quadratic functions, sufficient conditions on existence periodic Markovian processes are provided. The uniform continuit...