Stability, bifurcation and control of a predator-prey ecosystem with prey herd behaviour against generalist predator with gestation delay

TL;DR

This paper develops and analyzes a predator-prey model with prey herd behavior and a non-monotonic functional response, exploring stability, bifurcations, and control strategies through analytical and numerical methods.

Contribution

It introduces a novel predator-prey model incorporating prey herd behavior and a non-monotonic response, with stability analysis, bifurcation conditions, and a control method for population blow-up.

Findings

Established local stability of the coexistence equilibrium.

Derived conditions for Hopf bifurcation and its normal form.

Validated analytical results with numerical simulations.

Abstract

In this paper, we proposed a population model depicting the dynamics of a prey species showing group defence against a generalist predator. The group defence characteristic is represented by a non-monotonic functional response. We have established the local stability of the model around the co-existent equilibrium solution using a local Lyapunov function. Condition for existence Hopf bifurcation is obtained along with its normal form. Numerical simulations have been done to confirm the obtained analytical results as well as to validate the proposed model. Sensitivity analysis of the parameters is performed using Latin hypercube sampling(LHS)/partial rank correlation coefficient(PRCC). Blow-up in the population is controlled using the Z-type dynamic method.