Qualitative analysis of a predator–prey model with Holling type II functional response incorporating a constant prey refuge

Dynamical analysis on prey refuge in a predator-prey model with square root functional response

“…Similarly to the proof in [3,4], we have the following. For simplicity, we take the following scaling: t = 1 + hα (1 − m)x τ and then system (1.2) takes the following form (still denotes τ as t)…”

“…Numerical simulations indicate the more complex dynamical behaviors of the model than those with Holling II type functional response in which the origin is unstable (e.g. [2,4,7,8]). Fig.…”

“…Prey refuges are widely believed to prevent prey extinction and damp predator-prey oscillations. For example, Chen et al have shown that prey refuges having a stabilizing effect on predator-prey interactions incorporating a constant prey refuge and the dynamic behaviors deeply dependent on the prey refuge parameter m [3,4]. Kar [10] and Huang et al [7] have studied a Lotka-Volterra type predator-prey system with Holling type II response function and Holling type III response function, respectively, incorporating a constant proportion of prey using refuges mx, which protects mx of prey from predation.…”

Incorporating prey refuge into a predator–prey system with imprecise parameter estimates

“…Since Gause et al [3] and Maynard Smith [4] introduced a quantity x R of the prey that involves refuges, the concept of prey refuges has attracted the attention of ecologists and mathematicians because it exists extensively in predator-prey communities. A lot of literatures showed that prey refuges have significant effects on the population dynamic (see [5,6,7,8,9,10,11,12] in detail). Incorporating prey refuges in the above system, system (1.1) turns into…”

Codimension two and three bifurcations of a predator–prey system with group defense and prey refuge

“…The dynamics of some predator-prey systems with constant prey refuge have attracted some authors' attention, one can refer to [2,5,8,10,12,13,14] and the references therein, the effect of prey refuge on the stability and the existence of limit cycle of the corresponding systems has been discussed.…”