Complex dynamics and optimal harvesting strategy of competitive harvesting models with interval-valued imprecise parameters

Abstract

Considering that species in nature are affected by the complexity of the ecosystem, biological parameters present certain inaccuracy or uncertainty. Different species exhibit different living habits, so it is of certain interest to investigate species related imprecise parameters. Besides, from the perspective of scientific and reasonable exploitation and utilization of fishery resources, two types of two-species competitive models with species related interval-valued imprecise parameters and harvesting are established. Firstly, the influence of interval-valued imprecise parameters on the dynamic behavior of the system without harvest are analyzed. Then, for continuous harvesting system, the existence of bio-economic equilibrium is discussed, and the optimal harvesting strategy is obtained by using Pontryagin’s maximum principle. Next, for the system guided by weighted harvesting strategy, the existence and stability of the order-1 periodic solution are discussed. Besides, in order to find the harvesting strategy that maximizes the economic profit in the harvest process, an optimization problem is constructed according to the actual situation, and the optimal set values of the weight and threshold of the strategy are obtained. 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 competitive fishery resources in the imprecise parameter environment.