Scale-stage Structure Population Model Optimal Harvesting And Time-lag Impact Analysis

Based on the concept of sustainable development of biological resources and the practical problems in the field of optimal control,a more realistic size-stage-structured harvest model is established.Taking the harvest rate as the control variable and combining the economic value and the regulation cost,in this paper,we study the optimal harvesting control problem of a size-stage-structured popu-lation model so as to achieve the optimal harvesting policy that can be accepted in the economic and ecological resources sustainable development and utilization.In addition,in nature,the population and the population interact with each other and affect each other.A predator-prey model with size-stage-structured in predator is established,and the model is transformed into a time delay system by variable substitution.Furthermore,we study the impact of time delay on its dynamic behavior.The full text is divided into five parts:In the first part,we introduce the research background,research status,and the contents and significance of this pa-per.The second part gives the basic knowledge and theorems involved in this paper.In the third part,we study the optimal harvesting control problem of a size-stage-structured population model.We use the method of characteristic to show that this model can be reduced to a threshold delay equations model,which can be further transformed into a functional differential equations model by a sim-ple change of variables.Such simplification allows us to use the classical theory about functional differential equations and establish a set of sufficient conditions to investigate the existence and uniqueness of solutions.Secondly,based on compact-ness,convergence and extremum sequence analysis,we prove the existence of the optimal harvesting.A predator-prey model with size-stage-structured in preda-tor is established in the fourth part.By the method similar to in the third part,we mainly discusses the existence,uniqueness,positivity and boundedness of the global solution of the model,as well as the linearization and stability of equilibria,analysis of the influence of threshold delay on the stability of the system.To de-termine the range of threshold delay to guarantee the stability of the system.The last is the summary and future work.