https://doi.org/10.1140/epjp/s13360-025-06897-7
Regular Article
Impact of superpredation in a spatiotemporal predator–prey system: a model-based analysis
1
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, 711103, Howrah, West Bengal, India
2
Department of Mathematics, Ramsaday College, 711401, Amta, Howrah, West Bengal, India
3
Amrita School of Engineering, Amrita Vishwa Vidyapeetham, 560035, Bengaluru, India
Received:
16
June
2025
Accepted:
23
September
2025
Published online:
7
October
2025
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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
