Transient indicator of exploited communities at equilibrium in generalist predator–prey models
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, 711103, Howrah, West Bengal, India
2 Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu, India
Accepted: 21 October 2022
Published online: 5 November 2022
Most research articles on the exploited predator–prey dynamics study the asymptotic profile of steady states, bistability, limit cycles and bifurcations. In these cases, the disturbances (harvesting) can lead to transient amplification before decaying asymptotically. Therefore, a deep understanding of transient dynamics near steady state is crucial to guessing the dynamics of interacting species for disturbances on short time scales. Here, we study this transient indicator to a generalist predator–prey system with Holling type III functional response. The disturbances are produced by different harvesting strategies, including prey harvesting, predator harvesting, and simultaneous harvesting of both species. In the case of the existence of unique interior equilibrium, the stable steady state becomes reactive. The results become complicated when the system becomes bistable in nature. Between two stable coexistence states, one becomes reactive, and another remains non-reactive. But it is observed that disturbance made by harvesting in our system affects the transient behavior of the system making it more stable in nature in every case compared to the unharvested system. We also observe that the MSY policy is suitable for prey and simultaneous harvesting of both species in comparison with predator harvesting.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. 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.