Effect of delay and control on a predator-prey ecosystem with generalist predator and group defence in the prey species

TL;DR

This paper investigates how delay and control mechanisms affect the stability and dynamics of a predator-prey ecosystem with generalist predators and group defense, providing analytical and numerical insights.

Contribution

It introduces a stability analysis of a delayed predator-prey model with group defense and develops a feedback control method to stabilize unstable equilibria.

Findings

Derived Lyapunov stability criteria for the system

Identified conditions for Hopf bifurcation and bifurcation points

Demonstrated control mechanism restores stability

Abstract

Generalist predators consist an important component of an ecosystem which may act as a biocontrol agent and influence the dynamics significantly. In this paper, we have studied the effect of delayed logistic growth of the prey species with group defence behaviour. The Lyapunov stability criteria for the interior equilibrium point is derived. Also, the condition of Hopf-bifurcation and the point of bifurcation are obtained. The length of the delay is also estimated for the system to preserve stability. Numerical simulations are performed and illustrated to support the obtained analytical results. Using a feedback control mechanism, the stability of the unstable equilibrium point is restored. Latin Hypercube Sampling/Partial Rank Correlation Coefficient (LHS/PRCC) sensitivity analysis, which is an efficient tool often employed in uncertainty analysis, is used to explore the entire parameter space of a model.