Non-linear harvesting of prey with dynamically varying effort in a modified Leslie-Gower predator-prey system

Abstract

In this paper, a three dimensional dynamical system incorporating non- linear harvesting effort for prey is investigated. The Holling type-II functional response is considered for prey while predator is assumed to follow Modified Leslie-Gower type dynamics. The steady states of the system are obtained and the local dynamics is explored. The sufficient condition is derived for global stability of its positive interior equilibrium point. The conditions for bionomic equilibrium and uniform persistence of the system have been investigated. It is also observed that the system exhibits transcritical bifurcation for a threshold level of taxation. A taxation policy is discussed with the help of Pontryagin's Maximum Principle as an effective control instrument to preserve the prey species from extinction and maintain a sustainable fishery.

https://doi.org/10.28919/cmbn/2498