Complex dynamics of two prey–predator harvesting models with prey refuge and interval‐valued imprecise parameters

Abstract

In view of the phenomena that species in nature are affected by the complexity of the ecosystem, some key biological parameters have certain inaccuracy or uncertainty and part of the prey hides in the shelter from predation. Moreover, different species exhibit different living habits, so it is of certain interest to investigate species‐related imprecise biological parameters. Besides, from the perspective of scientific and reasonable exploitation and utilization of fishery resources, two types of harvesting strategies are introduced into the system. Firstly, the dynamic properties of the system guided by continuous harvesting strategy are analyzed, which demonstrates the impact of refuge rate, imprecision indexes and harvesting efforts on the system dynamics. Meanwhile, the bio‐economic equilibrium is discussed, and the optimal harvesting strategy is obtained. Secondly, the complex dynamics of the system induced by weighted harvesting activity are analyzed. The predator‐extinction periodic solution and coexistent order‐1 periodic solution is discussed according to different weights and thresholds. Finally, the correctness of the obtained results and the feasibility of the harvesting strategy are verified through numerical simulation in MATLAB. The results of this study provide a reference for the scientific and reasonable exploitation and utilization of prey–predator fishery resources in the imprecise parameter environment.