Stability analysis of prey predator model with Holling II functional response and threshold harvesting for the predator

Abstract

Abstract This paper deals with a prey predator model with Holling response function of type II and continuous threshold harvesting in the predator population. The prey grows as a logistic model when there is no interaction with the predator. The predator is assumed decreasing due to natural death and interspecific interaction when there is no interaction with its prey. The existence of the interior equilibrium point is considered and the stability is analysed using linearization and eigenvalues methods. The phase portrait of the model is also used to determine the behaviour of populations. From the analyses of the model with harvesting we found that there exists a stable interior equilibrium point. The predator population will remain sustainable when the size of the populations are initially close enough to the equilibrium point. But when the threshold value is too high and the populations are initially quite far from the equilibrium point, then the predator population may stop being harvested at a certain time. Some numerical simulations are given to confirm the result of analysis.