https://doi.org/10.1140/epjp/s13360-023-03824-6
Regular Article
Transient and asymptotic dynamics of Bazykin’s prey-predator model on managing reactivity, resilience, and maximum sustainable yield
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, 711103, Howrah, West Bengal, India
Received:
8
January
2023
Accepted:
13
February
2023
Published online:
18
March
2023
Ecologists historically have mainly concentrated on the long-term dynamics of ecological models. But, short-term dynamics are just as important as long-term dynamics because ecological systems cannot finish responding to a disturbance before the next one happens. This paper investigates the transient and asymptotic dynamics of Bazykin’s model. The model is the extended version of the Rosenzweig–MacArthur model by adding an intra-specific competition among predators. We mainly investigate the effect of prey and predator harvesting on the transient dynamics of the system. The sensitivity of reactivity is also examined using matrix calculus. Due to the analytical complexity of the coexisting equilibrium, numerical simulations are carried out to show most of the results. By increasing predator harvesting effort, the system can be made non-reactive while such transition was not detected in the case of prey harvesting. Using Sotomayor’s theorem, saddle-node bifurcation is seen. The system is highly reactive and less resilient in the vicinity of the saddle-node bifurcation. Moreover, the impact of intra-specific competition is also investigated. We conclude that the higher the harvesting effort, the lesser the intra-specific competition affects the reactivity and resilience of the system. Our sensitivity analysis intel that the sensitivity of reactivity depends on the parametric space.
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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.
