Dynamic Behaviors And Optimization Strategy Of Stochastic Population System With Hybrid Noises

The population system is full of the disturbance of environmental noise.Small disturbance is usually described by white noise,while large disturbance is mostly described by Markov chain.At the same time,the optimal harvesting strategy is of great significance to the development,management and utilization of ecosystems.Based on this,this paper mainly studies the dynamic behaviors of two kinds of population systems with hybrid noises,including the well posedness,stochastic persistence and stochastic stability of the system solution,and obtains the optimal harvesting strategies of two kinds of stochastic three species systems.The main contents are as follows:In the first part,a class of phytoplankton-zooplankton-fish three population model with hybrid noises and distributed delay is established.Firstly,the well posedness,stochastic boundedness,stochastic persistence,stochastic stability of the solution and the dynamic behavior of the attractor are studied.According to all cases of system parameters,the dynamic behavior of the population system is analyzed globally,and the theoretical threshold of extinction or average persistence(19 cases)of each species is obtained.At the same time,an optimal harvesting problem is proposed to pursue the maximum of total economic income,and the necessary and sufficient conditions for the existence of the solution of the optimization problem are obtained.The optimal solution of the problem is given.Finally,numerical simulations show the effectiveness of the results.In the second part,considering the influence of toxins on the population system in a polluted environment,a three species model with modified Holling II functional response and hybrid noises in polluted environment is established.The sufficient conditions for species extinction,strong mean persistence and mean stability are obtained from the asymptotic analysis of the system solution.Furthermore,the theoretical threshold between species mean persistence and extinction is found.What's more,taking the optimal harvesting effort as the decision variable,an optimal harvesting problem with the maximum sustainable output as the objective function is proposed,and the explicit expressions of the optimal harvesting effort and the maximum sustainable output are given.Finally,several numerical examples are given to verify the effectiveness of the proposed method.