Influence of Allee effect in prey populations on the dynamics of two-prey-one-predator model

Abstract

One of the important ecological challenges is to capture the complex dynamics and understand the underlying regulating ecological factors. Allee effect is one of the important factors in ecology and taking it into account can cause significant changes to the system dynamics. In this work we consider a two prey-one predator model where the growth of both the prey population is subjected to Allee effect, and the predator is generalist as it survives on both the prey populations. We analyze the role of Allee effect on the dynamics of the system, knowing the dynamics of the model without Allee effect. Interestingly we have observed through a comprehensive bifurcation study that incorporation of Allee effect enriches the local as well as the global dynamics of the system. Specially after a certain threshold value of the Allee effect, it has a very significant effect on the chaotic dynamics of the system. In course of the bifurcation analysis we have explored all possible bifurcations such as the existence of transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and Bautin bifurcation and period-doubling route to chaos respectively.

Pattern Formation in a Reaction‐Diffusion Predator‐Prey Model with Weak Allee Effect and Delay

“…We calculate the Jacobian matrix of model (5) at E * , which is given by J * � a 10 a 01 b 10 b 01 , where…”

“…Cai et al [6] established a Leslie-Gower predator-prey model with additive Allee e ect on prey, and they found Allee e ect can increase the risk of ecological extinction. Sen et al [5] established a twoprey one-predator model with Allee e ect, and the e ects of Allee e ect on the dynamics of predator population are discussed. Of course, the research on reaction-di usion predator-prey model with Allee e ect is also very rich.…”

Stability and Hopf Bifurcation of Three-Species Prey-Predator System with Time Delays and Allee Effect

“…Motivation to what we mentioned above, it is interesting and important to study the impact of time delays and Allee effect on the dynamics of three-species prey-predator models. In this paper, we extend the work in [26] and study the dynamics of a two-prey one-predator system, where the growth of both prey populations is subject to Allee effects, and there exists a direct competition between the two-prey species having a common predator. Two discrete time delays τ 1 and τ 2 are incorporated into the predator growth equation to represent the reaction time with each prey.…”

“…Many studies have been done on multispecies prey-predator systems, including local and global bifurcations and different types of chaos (see, e.g., [26][27][28][29]). Sen et al [26] discussed the Allee effect on two-preys' growth function, where the predator is generalized. ey explained how the Allee effect can suppress the chaotic dynamics and the route to chaos in prey growth by comparing it with a model without the Allee effect.…”

Stability and Bifurcation in a Predator–Prey Model with the Additive Allee Effect and the Fear Effect

“…For sparse populations experiencing the Allee effect, Dennis demonstrated with numerical simulations that the critical density, the growth, and the extinction probability can be obtained. Until now, many researchers have paid a great deal of attention on the impact of Allee effect on predation (see [7][8][9][10][11][12][13][14][15][16][17][18]). For example, Liu et al [9] showed that a system with gestation delay and an additive Allee effect is unstable if economic interest increases through zero, which may occur in the case of an Allee effect (strong or weak).…”