Dynamics of predator–prey system with fading memory

Abstract

A predator–prey model with fading memory for general Holling type functional response is proposed. The fading memory term is used with the hypothesis that the predator’s growth rate at present depends on the recent past quantities of prey. The effects of predator harvesting is also considered in the model. The model is analysed theoretically as well as numerically. Two parameter bifurcation analysis are done and the existence of Hopf point bifurcation is identified. Both supercritical and subcritical Hopf bifurcations are obtained with the variation of system parameters. Maximum sustainable yield with respect to harvesting effort is also determined. It is to be observed that the system dynamics is very rich in presence of fading memory. The obtained results may be useful in the field of agriculture and fishery.