Bifurcation analysis on predator-prey Leslie-Gower model holling respond function type II with harvesting on predator and prey population

Abstract

The objective of this research is to study Leslie-Gower predator-prey Holling respond function type II models on predator and prey population. In this predator-prey model it is assumed that there are harvesting efforts in both populations. The steps to analyze this models including to looking for equilibrium points, and analyzing the exchange the parameter of permanent harvesting value to know the possibility of bifurcation. Based on analysis obtained four equilibrium points which is the trivial equilibrium point E0, the equilibrium point E1 for the extinction of predator, the equilibrium point E2for the extinction of prey, and the endemic equilibrium point E3. The equilibrium points of E2 and E3 experiencing stability changes when the rate of harvesting parameter on prey population (H1) and predator (H2) is varied so that the system have a bifurcation. The forming of limit cycle on portrait phase around equilibrium points shows that the kind of bifurcation that happen was a Hopf bifurcation.