Fish Harvesting Models With State-dependent Feedback Impulse Control

With the development of science and technology,mathematical biology models has been widely applied in various fields,such as,biological technology,economy,agriculture,fish harvesting and other fields.In the past ten years,fish harvesting model with state-dependent feedback control is investigated in this paper.The topology of the space is not changed by equivalence transformation,and a two-dimensional system is used to study the one-dimensional system with the nature of the state.A linear approximation equation is used to study the stability of the equilibrium point of the system in the case of the fish harvesting model without impulses.The Dulac function method is used to prove the non-existence of the limit cycle of the system and to prove the global asymptotic stability of the unique positive equilibrium point of the system,using Lyapunov function method to prove that the only positive equilibrium point of the system is globally asymptotically stable.When there is a pulse in the fish harvest model,the impulse differential equation theory and geometric successor function method are used to study the impulsive dynamic behavior,to obtain the conditions for the existence of order 1period solution and the existence of order 1 period solution,and to prove that orbit of the order 1 period solution is asymptotically stable.The results show that a certain proportion of harvesting according to the fish density in the water is beneficial to the development of the population in the process of fish exploitation.Consider the objective actual situation,consider the existence of impulse state,it was found that the harvesting model is more realistic by using a semi-continuous dynamic system.Based on this,impulse are considered and state-feedback control is implemented for fish population release as well as harvesting at regular intervals,and capture is implemented based on the dynamics of the population size.Numerical simulations show that the harvesting model under state-dependent feedback control provides a more vivid picture of population development.Based on the modeling results and taking into account the actual situation,the implementation of stock harvesting does not affect the development of fish populations and implements exploitation management of fish population.