https://doi.org/10.1140/epjp/s13360-025-06589-2
Regular Article
Price-driven instability in marine fisheries: bifurcation analysis of harvested predator–prey systems
1
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, 210044, Nanjing, Jiangsu, China
2
Laboratory of Nonlinear Analysis and Applied Mathematics, Department of Mathematics, University of Tlemcen, 13000, Chetouane, Algeria
3
UMMISCO, Sorbonne Université, Institut de Recherche pour le Développement, IRD, 93143, Bondy, France
Received:
20
March
2025
Accepted:
23
June
2025
Published online:
8
July
2025
This paper presents a marine prey-predator community model with prey and predator fishing. Prices of the resources on the market are assumed to vary under the effect of supply and demand. The model takes into account five variables: the fishing effort, the biomass of prey and predator resources, and their corresponding market prices. Assuming a rapid variation in prices relative to the other mechanisms at play leads us to consider a slow-fast fishing model. Two main scenarios emerge: a catastrophic equilibrium (CE) in which overexploitation leads to the extinction of some or all biological populations, and a sustainable fishery equilibrium. Under some conditions, the system can exhibit cross-critical, saddle node and Hopf bifurcations. The bifurcation analysis shows that prey growth rate and predator natural mortality play an important role in the stability of equilibrium states of the system. In addition, we explore conditions to prevent extinction and restore sustainable fishing. A rational management policy can restore fishery stocks by disrupting the catastrophic equilibrium and maintaining the fishery at a stable positive equilibrium. This paper also considers the effects of taxation. By choosing the right tax rate, we show that the income of the fishery can be maximized. Finally, we show some numerical simulations to verify our analysis results.
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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.
