Hopf bifurcation and stability for predator–prey systems with Beddington–DeAngelis type functional response and stage structure for prey incorporating refuge

Abstract

Please cite this article as: F. Wei, Q. Fu, Hopf bifurcation and stability for predator-prey systems with BeddingtonDeAngelis type functional response and stage structure for prey incorporating refuge, Appl. Math. Modelling (2015), doi: http://dx.Abstract: A kind of stage-structured predator-prey model with Beddington-DeAngelis functional response incorporating a prey refuge is investigated in this paper. By analyzing the corresponding characteristic equations, the local stability of the equilibria is investigated. Moreover, Hopf bifurcations occur at the positive equilibrium as the delay τ crosses some critical values. Further, the influence of prey refuge on densities of predator species and prey species is investigated. Numerical simulations are carried out to illustrate our main results.

Protection zone in a diffusive predator–prey model with Beddington–DeAngelis functional response

“…In contrast, the protection zones, as refuges from humans, always benefit the endangered species. Refer to [15,16,21,25,28,29,30] for more backgrounds on prey refuges and their affections. In this paper, we will show the effect of the prey's refuge and the size of the protection zone on the coexistence and stability of the predator-prey system with B-D type functional response.…”

Stability and Hopf bifurcation for a stage-structured predator–prey model incorporating refuge for prey and additional food for predator

“…The delayed predator-prey models with stage structure or refuge have been studied by many authors, see [8][9][10][11][12]. Especially, Wei and Fu [13] investigated Hopf bifurcation and stability of a delayed predator-prey model with stage structure for prey incorporating prey refuge, ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ẋ 1 (t) = ax 2 (t)bx 1 (t)αx 1 (t), x 2 (t) = αx 1 (t)cx 2 (t)dx 2 2 (t) -…”

A non-autonomous Leslie–Gower model with Holling type IV functional response and harvesting complexity

“…In spite of a lot of works focused on the global dynamics and bifurcation analysis of the ecological systems (e.g., ), in realistic environment, ecological systems are usually affected by the seasonable perturbations or other unpredictable disturbances (e.g., see [24][25][26][27][28][29][30][31][32][33][34][35][36]). Thus the time-varying parameters are more reasonable when we try to consider the periodic environment.…”