Impact of superpredation in a spatiotemporal predator–prey system: a model-based analysis

In this study, we conduct a comprehensive analysis of a predator–prey system governed by a Holling type II functional response, wherein the presence of a superpredator modulates the growth dynamics of the predator. The primary objective of this research is to investigate the impact of the superpredator’s presence on the overall system dynamics. The equilibrium points and their stability properties are thoroughly examined for the nonspatial system, alongside a detailed investigation of Hopf bifurcation phenomena near the steady states. By incorporating self-diffusion and cross-diffusion terms, the modified spatiotemporal model is rigorously examined through analytical techniques and numerical simulations under periodic boundary conditions on a square domain. The study further investigates the conditions for diffusion-driven instability alongside a detailed exploration of Hopf and Turing bifurcation regions within a two-parameter space. A series of numerical simulations is presented for biologically meaningful parameter values, illustrating the emergence of diverse spatial patterns, including spots, stripes, stripe–spot mixtures, and labyrinthine structures within the Turing space. These results highlight the pivotal role of the superpredator’s maximum consumption rate in governing the system’s spatial dynamics and determining the eventual ecological configuration. It is further observed that the predator’s natural mortality rate and the carrying capacity coefficient of the prey significantly influence the pattern dynamics in the presence of a superpredator.