https://doi.org/10.1140/epjp/s13360-023-04651-5
Regular Article
Exploring resilience, chaos, and bifurcations in a discrete food web model incorporating the mate finding Allee effect
1
Department of Applied Mathematics, University of Calcutta, 700009, Kolkata, India
2
Department of Mathematics, JIS College of Engineering, 741235, Kalyani, India
3
Department of Mathematics, University of Kalyani, 741235, Kalyani, India
4
Department of Mathematics, College of Science, King Khalid University, 61413, Abha, Saudi Arabia
Received:
12
September
2023
Accepted:
31
October
2023
Published online:
15
November
2023
In this paper, we present a comprehensive investigation of a discrete food web model enriched with mate finding Allee effects and hunting cooperation. Our study encompasses an in-depth analysis of feasible equilibria within the proposed ecological system and their stability properties. To uncover the intricate dynamical behaviors of this system, we employ mathematical tools such as the center manifold theorem to explore different bifurcations. To validate our analytical findings and provide a visual representation of the system’s behavior, we offer a range of numerical examples, including bifurcation diagrams, MLEs, phase diagrams, and solutions trajectories. Our results reveal that, under conditions of low prey growth, the predator population cannot persist in the system. Additionally, we observe intriguing dynamics in the growth rate, characterized by Neimark–Sacker, flip, and period-doubling bifurcations. Furthermore, the mate finding Allee parameter introduces chaos into the system, transitioning from one period to two periods to multiple periods. Notably, a higher growth rate of prey appears to control the chaos induced by the Allee parameter. Moreover, the populations in the proposed model exhibit resilience to external perturbations. This study underscores the importance of considering complex ecological interactions and cooperation in predator–prey systems, shedding light on their stability and dynamic behavior under various conditions.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. 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.