https://doi.org/10.1140/epjp/s13360-025-06182-7
Regular Article
Asymptotic and transient approaches of harvested predator–prey models with reaction–diffusion
1
Department of Mathematics, Indian Institute of Engineering Science and Technology, 711103, Shibpur, West Bengal, India
2
Department of Mathematics, Shibpur Dinobundhoo Institution (College), 711102, Howrah, West Bengal, India
Received:
15
July
2024
Accepted:
28
February
2025
Published online:
16
April
2025
This article proposes a diffusive predator–prey model with the Allee effect in predator and harvesting efforts on both species. Allee effect and harvesting efforts are taken as control parameters. Due to more than one control parameter, the asymptotic and short-term dynamics are analyzed, dividing the model into three sub-models. The stability analysis and bifurcation of all models’ interior equilibrium are duly reported for the temporal system. The model system’s analytical outcomes are validated numerically through their graphical representations. Besides, in the spatial system, the Turing bifurcation condition is derived. We see that all three systems are always reactive. By observing the changes in reactivity, we see that both the harvesting efforts and the ‘Allee effect constant’ have destabilizing effects. This causes a reduction in the density of the predator species. Various rich spatial patterns, including spots, stripes, and labyrinthine, are detected using numerical simulations. Generally, researchers study long-term dynamics when analyzing spatial systems. With the help of short-term dynamics, we have established the system is always reactive, and it is in increasing mode at turning regions in all subcases. These results are also verified numerically. This resemblance is the main outcome of this work.
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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.
