Can Prudent Predation Promote Species Coexistence in a Prey-Predator Model with Additive Allee Effect and Fear Factor?

Abstract

In this paper, we study the influence of the prudence level on the dynamics of a predator-prey model incorporating the additive Allee effect and the fear factor. First of all, we prove the positivity and boundedness of the system solution. Then we investigate the existence and local stability of equilibria and prove the global stability of the positive equilibrium using the Dulac Theorem. Furthermore, we also demonstrate the occurrence of various bifurcations, such as saddle-node, transcritical, and Hopf bifurcations. These theoretical results are proved with numerical simulations. Through numerical simulations, we find the following. (i) An appropriate level of prudence and a weak Allee effect can improve the system stability and promote the coexistence of predators and prey. However, a strong Allee effect may lead to the extinction of predators. (ii) When the level of prudence exceeds a certain threshold, predators will become extinct, but this threshold will increase as the Allee effect level decreases.

Keywords

Additive Allee effect / Fear factor / Prudent / Predator-prey model / 34D23 / 92D25 / 92D45

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Shanghai University