Qualitative Analysis Of Two Types Of Population Models With Discontinuous Acquisition Strategies

The utilization and protection of the population is of great concern, and the control strategy is particularly important. The studies focused on the continuous mathematical model, and practical application in discontinuous harvest is in the majority. So in this paper, the theory of discontinuous differential equation mathematical model is established, based on discontinuous strategy, for single and two species of qualitative analysis and control.First of all, for a class of discontinuous strategy containing single population model and qualitative analysis,we introduced in the model block factor and discontinuous function, the use of differential inclusions, Filippov solutions and measurable selection theorem into discontinuous model; using integral equation, comparison principle, T-D principle and Lyapunov function respectively model with persistence and stability, and the above conclusion; through the definition of a discontinuous function and benefits of functional model gives specific control methods; finally, we have given the three case of numerical simulation and the track change trend for continuous and discontinuous models, this chapter generalizes Guo Zhenyuan's conclusion, the research methods and ideas has the advantage over the continuous differential equation in single population control.Secondly, the qualitative analysis and control of the two species model with Hollingll type populations are considered in the case of non continuous capture. And using the differential inclusion, measurable selection theorem discontinuity model transformation of Filippov solutions; qualitative analysis using the Hurwitz criterion and the Lyapunov function, the analysis in the process of considering the shelter effect of positive equilibrium point exists, local stability and global stability of the impact, there is a need for global asymptotic stability of the conclusion is obtained. Finally, the specific control strategy of the model is given by the definition of the discontinuous function and the income function, and the control problem of the prey predator population is solved by using the discontinuous differential equation.