Maturation delay induced stability enhancement and shift of bifurcation thresholds in a predator–prey model with generalist predator

Discrete time delay has been widely used in models of interacting populations to capture various biological processes such as gestation, maturation, food digestion, disease transmission and so on. In most of the works, it has been demonstrated that a longer maturation delay is responsible for the destabilization of the coexistence steady-state. The constructed model system, however, may produce different phenomena if the maturation delay is included in an ecologically justified way, preventing the model from producing inconsistent results. Previous studies focus on the influence of delayed maturation in predator–prey dynamics with specialist predators mostly. The primary goal of this article is to explore how delayed maturity in generalist predators qualitatively affects the dynamics of a predator–prey system. To illustrate, we consider a predator–prey model with generalist predators and Holling type II functional response to characterize the generalist predator’s grazing behavior toward their primary prey. We find various parameter regimes for the non-delayed system where we see either no coexistence, single coexistence, or multiple coexistence of prey and their generalist predators. Rich dynamics, induced by various local and global bifurcations, are displayed for the non-delayed system. The inclusion of a maturation delay in the model system causes the system’s qualitative properties to alter, such as shifting bifurcation thresholds and a reduction in the region of multi-coexistence in a parametric domain. Our analysis demonstrates that the delayed maturation of generalist predators does not act as a destabilizing factor; instead, it promotes stable coexistence. Visual depictions of all the analytical findings have been presented through extensive numerical simulation and the ecological implications of the obtained results are summarized in the concluding section.