Dynamics of a prey-predator system under the influence of the Allee effect and Holling type-II functional response

Abstract

Capturing complicated dynamics and understanding the underlying controlling ecological processes is one of the major ecological issues. The Allee effect is an essential component in ecology, and considering it can have a substantial impact on system dynamics. In the present investigation, we analysed a prey-predator scenario in which the predator is a generalist since it feeds on prey populations and the Allee phenomenon impacts the prey population's growth. The influence of the Allee effect on the changing nature of the system is investigated. The stability and boundedness of the model's equilibria are extensively investigated. We found that including the Allee effect enhances the system's local and global behaviours through a detailed bifurcation analysis. The chaotic nature of the system is strongly impacted by the Allee effect, particularly once a specific threshold value is reached. In the study of bifurcation analysis, we looked into bifurcations such the presence of transcritical bifurcation and Hopf-bifurcation to chaos. We added stochastic perturbation to this problem by including random fluctuations in the sensitive parameters. Finally, we analysed the system's mean-square stochastic stability towards the internal equilibrium. As a result, it is discovered that the Allee effect and stochastic perturbation considerably influence the behaviour of the prey-predator system.

Keywords

• predator-prey model
• allee effect
• transcritical bifurcation
• stochastic stability