Study on dynamic behavior of two fishery harvesting models: effects of variable prey refuge and imprecise biological parameters

In natural systems, the change of ecological environment can indirectly affect some key biological parameters of species and their activity patterns, among which the imprecision of biological parameters and prey refuge behavior are two more obvious embodiments. The aim of this work is to investigate the triple effects of imprecision of biological parameters, prey refuge behavior and fishing activities on the dynamics of the system. Firstly, a novel Ivlev's type fishery model incorporating with variable prey refuge and imprecise parameters is proposed. The dynamic properties of the fishery model under continuous fishing mode are analyzed, and the effects of variable prey refuge, imprecise index and fishing effort on the existence and stability of equilibrium are given. Moreover, the bionomic equilibrium and optimal fishing strategy are obtained. Secondly, from the perspective of reasonable exploitation of fishery resources, the weighted fishing strategy is introduced into the system, and the relevant weights and thresholds can be adjusted according to the actual demand, which is conducive to the sustainable development of fishery resources. The dynamic behavior of the fishery model under weighted fishing model is discussed, including the existence and stability of predator-extinction periodic solution and co-existence order-1 periodic solution under different fishing thresholds and weights, which not only provides a possibility to fishing species according to the period, but also ensures a certain robustness of the fishing strategy. Finally, to illustrate the theoretical results, numerical verifications for two harvesting models are presented to demonstrate the impact of variable prey refugia, imprecise biological parameters and fishing efforts on the behaviors of the system. The results of this study provide a reference for the scientific and reasonable exploitation and utilization of fishery resources in an imprecise environment.

Automated summary

This study investigates the triple effects of imprecision of biological parameters, prey refuge behavior, and fishing activities on the dynamics of the system. A novel fishery model is proposed, incorporating variable prey refuge and imprecise parameters. The dynamic properties of the model are analyzed, and the effects of different factors on equilibrium existence and stability are discussed. Additionally, the introduction of the weighted fishing strategy promotes sustainable development of fishery resources. Numerical verifications are conducted to demonstrate the impact of these factors on the system's behavior.