https://doi.org/10.1140/epjp/s13360-025-06939-0
Regular Article
Dynamical complexities in a food chain model with schooling behavior: a study in a parameter plane
1
Department of Basic Science and Humanities, Indian Institute of Information Technology, 813210, Bhagalpur, India
2
Department of Mathematics, Visva-Bharati, 731235, Santiniketan, India
a
nikhil.pal@visva-bharati.ac.in
Received:
21
August
2025
Accepted:
6
October
2025
Published online:
18
October
2025
The food chain provides crucial insights into the intricate interdependencies within ecosystems, guiding effective conservation and management strategies. The primary goal of this study is to investigate the dynamical complexities of a deterministic tri-trophic food chain model where the interaction between the prey and the middle predator is described using the Holling type-II response function, whereas Cosner functional response is used to describe the interaction between the middle and top predators. Bifurcation, Lyapunov exponent, and isospike diagrams reveal various kinds of dynamical behaviors of the system. Shrimp-shaped and spiral shrimp-shaped domains are observed in the chaotic zone of the parameter plane. The coexistence of various types of attractors and spike-bubbling phenomenon are also observed. The corresponding stochastic model is also studied in the presence of environmental noise. This study offers valuable information about the persistence and conservation of species in both deterministic and stochastic environments.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjp/s13360-025-06939-0.
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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.
