https://doi.org/10.1140/epjp/s13360-024-05543-y
Regular Article
Bifurcation and pattern formation in a prey–predator model with cooperative hunting
Department of Mathematics, National Institute of Technology Patna, 800005, Patna, Bihar, India
Received:
3
June
2024
Accepted:
6
August
2024
Published online:
15
August
2024
In this article, we have investigated the temporal and spatiotemporal dynamics of the prey–predator model with hunting cooperation. Prey–predator models contribute to the field of mathematical biology by providing concrete examples of nonlinear dynamics, bifurcations, and chaos theory. These models explain the conditions under which populations remain stable or exhibit oscillatory behavior. They help us identify factors that lead to population cycles and stability. Predator control prey populations, preventing overgrazing or overpopulation, while prey availability influences the predator’s number. Cooperative hunting plays an important role in regulating prey–predator populations. It involves predator working in groups to hunt prey, improving their hunting efficiency compared to solitary hunting. In this paper, we consider a spatial and non-spatial prey–predator model with a Holling type IV functional response and cooperative hunting. The temporal model shows different kinds of bifurcations, such as Hopf, transcritical, homoclinic, saddle-node, and Bogdanov–Takens (BT) bifurcations. After examining the bifurcation properties, we proceed to enrich our model by introducing diffusion in both one and two dimensions, aiming to investigate the emergence of Turing and non-Turing patterns. They help us in understanding spatial patterns and structures that arise in nature, such as animal territories, vegetation patterns, and the distribution of organisms. The result of the numerical simulation shows that the model exhibits different kinds of Turing patterns, such as spots, a mixture of spots and stripes, and labyrinthine patterns in the pure Turing region, while spiral pattern in the non-Turing region.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.
