Effect of delay and control on a predator–prey ecosystem with generalist predator and group defence in the prey species
Department of Mathematics, NIT Durgapur, 713209, Durgapur, India
2 Department of Mathematics, Faculty of Science and Technology, ICFAI University Tripura, Kamalghat, 799210, Mohanpur, West Tripura, India
Accepted: 26 November 2021
Published online: 15 December 2021
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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021