Dynamical Behavior of a Delayed Holling Type‐II Predator‐Prey Model with Predator Cannibalism

Abstract

In this article, we propose the Holling type-II predator-prey model involving cannibalism and gestation delay in predators. We study the existence of all possible equilibrium points of the proposed model. We give the condition for the local stability and Hopf bifurcation analysis for the nondelayed model. Next, we also establish the local stability and Hopf bifurcation analysis for the corresponding delayed model. Finally, we discuss how cannibalism and delay play an important role in stabilizing and destabilizing the proposed system both theoretically and numerically.

Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback

“…Regarding the delay as bifurcating parameter, they discussed the local asymptotic stability and Hopf bifurcation of the positive equilibrium by analyzing the corresponding characteristic equations of linearized systems. Lavanya et al [30] proposed the Holling type-II predator-prey model involving cannibalism and gestation delay in predators and gave the condition for the local stability and Hopf bifurcation analysis for the non-delayed model. Taffo and Siewe [31] examined dynamical behavior of a nonlinear oscillator with symmetric potential that models a quarter-car forced by the road profile under parametric excitation.…”

“…Lavanya et al. [30] proposed the Holling type‐II predator‐prey model involving cannibalism and gestation delay in predators and gave the condition for the local stability and Hopf bifurcation analysis for the non‐delayed model. Taffo and Siewe [31] examined dynamical behavior of a nonlinear oscillator with symmetric potential that models a quarter‐car forced by the road profile under parametric excitation.…”

The Effect of Fear on a Diseased Prey–Predator Model with Predator Harvesting

“…Predator-prey interactions have been included in the Lotka-Volterra model for a very long time, see references [1][2][3]. In a similar vein, after the seminal work of Kermack and McKendrick [4], the interaction of the susceptible, infected, and recovered prey has been an interesting topic of study. The original predator-prey model was developed in large part by Vito Volterra and Alfred James Lotka.…”