Delayed carrying capacity induced subcritical and supercritical Hopf bifurcations in a predator–prey system

Abstract

The effects of past activities of prey population on the dynamics of a predator–prey system are explored by introducing a delayed carrying capacity of the prey. The delay-induced stability changes, bifurcation patterns, and long-term dynamics are studied. The delay instigates three types of stability scenarios at the coexisting steady state: no stability change, stability change (stable to unstable only), and stability switching, depending on the other parameters. This is one of the novelties of the present study in obtaining all these results in a single model with a single time delay. The relationships between delay and other system parameters for the existence of the stability scenarios are established analytically. Nature of the bifurcations is determined using normal-form reduction. Another important contribution is to unveil the occurrence of delay-induced subcritical and supercritical, non-degenerate and degenerate Hopf bifurcations around the coexisting steady state. Finite-time oscillation death resulting in mass extinction of populations is observed in the unsteady regime. © 2022 International Association for Mathematics and Computers in Simulation (IMACS)