One-parameter bifurcation analysis of prey-predator model with harvesting strategies

Abstract

This study investigates the effect of changes in the parameter of harvesting effort in both prey and predator species. As we know, prey and predator correlate to each other. Thus, it is important to know the dynamics of their population when the interaction is affected by the harvesting activity. To do this, we consider an ecological model of prey-predator interactions with the presence of harvesting effort. Then, we employ stability analysis, bifurcation analysis and numerical simulations to illustrate the dynamical behaviours of the prey-predator system. This study also analyses the behaviour of prey-predator interactions as the harvesting parameters of prey and predator species are varied. With the help of mathematical software such as XPPAUT and Matlab, a few graphs of bifurcation, phase plane, and time series are plotted. Maple software is used to find the Jacobian matrix and also the critical points. By using bifurcation analysis, there is an occurrence of one transcritical bifurcation point. Our finding demonstrates that as the harvesting parameter exceeds the transcritical bifurcation point, the prey-predator system changes from stable to unstable or vice versa.