https://doi.org/10.1140/epjs/s11734-026-02123-2
Regular Article
Study on fear-induced group defense and cooperative hunting: bifurcation, uncertainty, seasonality, and spatio-temporal analysis in predator–prey system
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, 711103, Howrah, India
a
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Received:
11
August
2025
Accepted:
5
January
2026
Published online:
31
January
2026
Abstract
The dynamics of predator–prey systems, particularly in the context of cooperative hunting by predator and resulting fear felt by prey population, provide significant ecological relevance. In the context of predator–prey dynamics, it is observed that predator affects prey population through two primary mechanisms: direct mortality resulting from predation, and due to predation fear in prey species, which subsequently enforces them to implement various anti-predation strategies. Group defense strategies benefit prey by lowering predation risk; however, it concurrently diminishes their reproductive potential. The well-posedness and stability analysis of the system have been rigorously performed. Bifurcation analysis indicates the presence of multiple local bifurcations within the system, specifically transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation. Furthermore, our study delineates the two-dimensional bifurcations, including Bogdanov–Takens, generalized Hopf and cusp bifurcations, for various parametric combinations. Latin hypercube sampling is applied to perform uncertainty analysis on input parameters, with the objective of examining their impacts on population dynamics. Following this, Kendall and Spearman rank correlation coefficients are calculated to determine the influence of these uncertainties on the population. By choosing appropriate parameter values, we have studied the nonautonomous case of our formulated system and found the chaotic, periodic and quasiperiodic behavior of the system. The latter portion proposes a spatio-temporal system with two-dimensional diffusion terms to determine Turing instability criteria and also exhibits the presence of spatio-temporal chaos. We have performed numerical simulations to investigate spatial patterns. The investigation provides substantial insights into the dynamics of intricate ecological systems, demonstrating the influence of spatial and temporal variables on predator–prey interactions and population dynamics.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2026
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.
