DYNAMICS AND BLOW-UP CONTROL OF A LESLIE–GOWER PREDATOR–PREY MODEL WITH GROUP DEFENCE IN PREY

Abstract

In this paper, we designed a population model that shows how a prey species defends itself against a generalist predator by exhibiting group defence. A non-monotonic functional response is used to represent the group defence functionality. We have demonstrated the model’s local stability in the vicinity of the coexisting equilibrium solution employing a local Lyapunov function. Condition for existence of Hopf bifurcation is obtained along with its normal form. The suggested model has been validated by numerical simulations, which have also been used to verify the acquired analytical results. The parameters are subjected to sensitivity analysis by utilizing partial rank correlation coefficient (PRCC) and Latin hypercube sampling (LHS). The Z-type dynamic method is used to prevent population blow-up.