Predator-prey dynamics with Allee effect on predator species subject to intra-specific competition and nonlinear prey refuge

Abstract

A modified version of our previously analyzed prey-predator refuge model is presented in this article by introducing Allee effect on the predator species and mutual interference among the predators. Possible number of coexistence equilibrium points are investigated with the help of prey and predator nullcline. The local stability and Hopf-bifurcation conditions are established around the coexistence equilibria. We have also discussed the nature of Hopf-bifurcation around the unique coexistence equilibrium point of the system as well. Finally, a comprehensive numerical simulation is carried out to justify our obtained analytical findings.

Dynamic Behaviors of an Obligate Commensal Symbiosis Model with Crowley–Martin Functional Responses

“…Let (x(t), y(t)) be any solution of system (33) with initial conditions x(0) > 0, y(0) > 0. similarly to the analysis of ( 37)- (40), for any ε > 0 small enough such that inequality (47) holds; there exists a T > 0 such that the following is the case.…”

“…As for as functional response is considered, there are many type functional responses on predator prey system. In his pioneering work, Holling [38] argued that, in the predator prey system, functional response should take into consideration; from then on, numerous works (see, for example, [39,40]) were been performed on Holling type II and III functional response. Noting that the predators hunt for food resources and as a consequence they have to share food or involve intra-specific competition, to describe this phenomenon, a ratio-dependent functional response [41] was introduced, and the functional response is dependent on both predator and prey species instead of only prey dependent functional response.…”

Modeling and Analyzing the Influence of Fear on the Harvested Modified Leslie-Gower Model

“…On the other hand, harvesting, as well as other biological factors such as the Allee effect and refuge, are important and common events [17][18][19][20] . Recently, researchers have looked into how refuge, Allee, and intra-specific competition among predators may impact the stability, bifurcation, and equilibria that affect the dynamic of prey-predator systems 21 . They concluded that an increase in intraspecific competition coefficient values stabilizes the dynamic system.…”

An Eco-Epidemiological Model Incorporating Harvesting Factors

“…Anderson and May [9] were the first to combine the two sciences and develop a predator-prey model with population illness. Many publications [10][11][12][13][14], Wang et al [15] examined numerous predator-prey models in the presence of infection in the system, and it was found that the illness is propagated by either prey or predator, or both prey and predator. The infectious illness divides prey-predator models into three categories.…”