Dynamic analysis of two fishery capture models with a variable search rate and fuzzy biological parameters

The fishery resource is a kind of important renewable resource and it is closely connected with people's production and life. However, fishery resources are not inexhaustible, so it has become an important research topic to develop fishery resources reasonably and ensure their sustainability. In the current study, considering the environment changes in the system, a fishery model with a variable predator search rate and fuzzy biological parameters was established first and then two modes of capture strategies were introduced to achieve fishery resource exploitation. For the fishery model in a continuous capture mode, the dynamic properties were analyzed and the results show that predator search rate, imprecision indexes and capture efforts have a certain impact on the existence and stability of the coexistence equilibrium. The bionomic equilibrium and optimal capture strategy were also discussed. For the fishery model in a state-dependent feedback capture mode, the complex dynamics including the existence and stability of the periodic solutions were investigated. Besides the theoretical results, numerical simulations were implemented step by step and the effects of predator search rate, fuzzy biological parameters and capture efforts on the system were demonstrated. This study not only enriched the related content of fishery dynamics, but also provided certain reference for the development and utilization of fishery resources under the environment with uncertain parameters.