Qualitative analysis of a harvested predator-prey system with Holling-type III functional response incorporating a prey refuge

Abstract

A predator-prey model with simplified Holling type III response function incorporating a prey refuge under sparse effect is considered. Through qualitative analysis of the model, at least two limit cycles exist around the positive equilibrium point with the result of focus value, the Hopf bifurcation under a prey refuge is obtained. We also show the influence of prey refuge. Numerical simulations are carried out to illustrate the feasibility of the obtained results and the dependence of the dynamic behavior on the prey refuge. Through the results of computer simulation, it is further shown that under certain conditions the model has three limit cycles surrounding the positive equilibrium point.

Global Dynamics of an Exploited Prey-Predator Model with Constant Prey Refuge

“…Ji and Wu [14] considered a predator-prey model incorporating a constant prey refuge and a constant-rate prey harvesting and showed that the system is controlled by using constant harvesting or prey refuge. Prepredator interactions with prey refuge also may be found in the work of Huang et al [15], Wang and Pan [16], Kar et al [17], and so forth.…”

Dynamical Behavior of a Predator-Prey System Incorporating a Prey Refuge with Impulse Effect

“…Mondal and Samanta [10] investigated the model with prey refuge dependent on both species and constant harvest in predator [10] and the model with nonlinear prey refuge [11,12]. Many models with prey refuge have been studied; one can also refer to [13][14][15][16][17][18][19][20][21] and the references cited therein.…”

Research on Rumor-Spreading Model with Holling Type III Functional Response

“…Holling proposes three kinds of functional response functions, which play an important role in predator-prey system [22,23]. Some scholars have studied the dynamics system with Holling type III functional response [24][25][26][27]. A rumor-spreading model with Holling-II functional response was established by Huo et al [28].…”