Dynamic modeling, analysis, and control of fish ecosystems are important for promoting the sustainable development of fish stocks. The objective of this study is to analyze the dynamic behavior of prey-predator systems with discontinuous prey refuge effect and different types of harvesting activities in an uncertain environment. Initially, a Filippov-type prey-predator model with fuzzy parameters is formulated and the positivity and bounded-ness of the solutions and the dynamic properties of Filippov prey-predator system are discussed. Next, from the perspective of effective exploitation and utilization of fish resources, a state linearly dependent fishing strategy is adopted into the system and a fishing model based on threshold feedback is established, as well as an analysis on the complex dynamics of the control system. Finally, to illustrate the theoretical results, computer simulations are presented step by step with an explanation on the practical significance. This study provides a reference for in-depth understanding of the development dynamics of fish resources and scientific planning of fishery resources exploitation.

In natural ecosystems, the external environment is constantly changing, and is affected by various factors, thus presenting a certain degree of randomness and uncertainty. Therefore, having a suitable habitat is essential for the reproductive success of many species. Understanding the impact of habitat selection provides valuable insights into how species locate and adapt to suitable living environments based on their specific needs. For this purpose, a prey-predator system model with prey habitat selection in an environment subject to stochastic disturbances is formulated. The properties of the proposed model without and with stochastic disturbances are investigated, including the existence of a unique ergodic stationary distribution, the stochastically ultimate bounded-ness of the solutions, and the extinction and persistence of the populations. The study demonstrates that prey can persist at a low intensity noise, whereas stronger stochastic disturbances may lead to the extinction of both the prey and predator species. To illustrate the theoretical results, numerical simulations are presented step by step. This work provides a theoretical reference for further studies on populations with habitat selection in an environment subject to stochastic disturbances.

In natural ecosystems, population dynamics are influenced by white and colored noise, which drive the population system to transition between multiple states. Therefore, it is essential to investigate predator-prey models that incorporate the concurrent impacts of white and colored noise. In this paper, we examined a three-dimensional stochastic predator-prey model involving dual prey species and a single predator by incorporating the refuge effect and habitat selection behavior under Markovian switching. By leveraging the theoretical framework of stochastic differential equations, its stochastic persistence was analyzed. Additionally, by constructing suitable Lyapunov functions, the conditions for an ergodic stationary distribution were deduced. Additionally, the extinction of populations and the asymptotic properties of solutions were explored. The findings revealed that habitat selection behavior has a significant and detrimental impact on the corresponding prey, while the refuge effect positively influences the prey and the predator. Ultimately, numerical simulations were performed to validate the theoretical outcomes. The results of these simulations strongly confirm the accuracy of the theoretical deductions.

The Allee effect is an important mechanism in ecosystems and a realistic description of the interaction between species. The study of the predator-prey model with the Allee effect is of great significance to promote the development of marine ecology. In this work, three aspects of studies are presented: Modelling and analysis: a predator-prey fishery model with the Allee effect in prey and generalist predator is first established. The existence, type, and stability of the boundary equilibria as well as the number of interior equilibria of the proposed model are discussed. Parameter influence: the bifurcations in the predation system are analyzed by selecting the capture rate of prey by the predator and Allee threshold as key parameters, and the results show that the system will undergo saddle-node bifurcation and Bogdanov-Takens bifurcation of codimension at least 2 and 3. Control measures: a bilateral intervention strategy is adopted for the capture and protection of marine fish. The existence and stability of the order-1 periodic solution and the order-2 periodic solution of the control system are analyzed by using the differential equation geometry theory. Additionally, numerical simulations are carried out to verify the correctness of the conclusions, and illustrate the impact of the Allee effect and bilateral intervention on the ecosystem, which provides an effective method for modern fishery conservation and harvesting.