Dynamics of a Leslie-Gower type predator-prey system with herd behavior and constant harvesting in prey

TL;DR

This paper explores how herd behavior and constant prey harvesting influence the complex bifurcation dynamics of a Leslie-Gower predator-prey model, revealing multiple bifurcation types that affect ecological diversity and economic sustainability.

Contribution

It demonstrates that herd behavior combined with prey harvesting induces diverse bifurcations, significantly altering the predator-prey system's dynamics compared to classical models.

Findings

Multiple bifurcations identified, including saddle-node and Bogdanov-Takens bifurcations.

Herd behavior and harvesting significantly impact ecological stability.

Results suggest strategies for ecological management and economic benefits.

Abstract

In this paper, the dynamics of a Leslie-Gower type predator-prey system with herd behavior and constant harvesting in prey are investigated. Earlier work has shown that the herd behavior in prey merely induces a supercritical Hopf bifurcation in the classic Leslie-Gower predator-prey system in the absence of harvesting. However, the work in this paper shows that the presence of herd behavior and constant harvesting in prey can give rise to numerous kinds of bifurcation at the non-hyperbolic equilibria in the classic Leslie-Gower predator-prey system such as two saddle-node bifurcations and one Bogdanov-Takens bifurcation of codimension two at the degenerate equilibria and one degenerate Hopf bifurcation of codimension three at the weak focus. Hence, the research results reveal that the herd behavior and constant harvesting in prey have a strong influence on the dynamics and also contribute to promoting the ecological diversity and maintaining the long-term economic benefits.