https://doi.org/10.1140/epjp/s13360-024-05282-0
Regular Article
Mathematical Modeling of Regime Shifts in Fluctuating Environments: The Impact of Allee Effects and Cooperation
1
Department of Mathematics, Government General Degree College, Chapra, 741123, West Bengal Nadia, India
2
Department of Applied Mathematics, University of Calcutta, 700009, Kolkata, India
Received:
29
March
2024
Accepted:
15
May
2024
Published online:
5
June
2024
In this paper, we investigate the deterministic and stochastic behaviour of the prey-predator model with cooperation and the mate-finding Allee effect. The stochasticity in the prey-predator model arises due to environmental or genetic fluctuations. The deterministic model is reduced to a stochastic model through the introduction of environmental fluctuations in model parameters. We discussed the dynamical behaviour of deterministic prey-predator models such as positivity, boundedness, different types of equilibrium and their local stability with different bifurcations. By allowing both prey and predator species to be affected by stochastic perturbations, we modify the proposed model to its stochastic counterpart. We investigate the uniqueness of positive global solutions, the existence of stationary distributions, etc., of stochastic model solutions. The simulation results for the stochastic system demonstrate that fluctuations in the ecosystem due to stochastic perturbations are highly sensitive to environmental noise intensities. With the increase in environmental fluctuation, there is a shift in regime i.e., noise-induced transition from the attractor to predator extinction. Stochastic confidence ellipses are used to analyze the effect of noise-induced transitions.
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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.
