Analysis And Extension Of A Class Of Continuous Hierarchial Age-structured Population Model

The evolutional behaviors of a population includes the recruitment of new-born in-dividuals and the death of old ones,which makes differences such as age,body size and dominance ranks widely observed.In order to describe the hierarchical age structure,most models in the literature assume that older individuals are more competitive than y-ounger ones.In some situations,however,the opposite is true.Based upon this fact,this dissertation is concerned with a hierarchical age-structured population model,which is a partial integro-differential equation with a global feedback boundary condition,and we assume that youngers are more dominant in competition process.We study the basic properties of model solutions,and the continuity of the solutions in harvest intensity.The stability of zero equilibrium is discussed and the existence of positive equilibria is shown.The well-posedness and continuous dependence of the solutions to the boundary control model are analyzed;and some numerical experiments are carried out to verify the theo-retical results.The main research work of this dissertation is divided into two parts:chapters 2 and 3.The second chapter focuses on system analysis.In section 1,we propose the basic model and make some assumptions.The next section contains the basic properties of the solutions of the model,such as the existence,uniqueness and boundedness of the non-negative solutions.The tools used are integral inequality and fixed-point theorem.We also investigate the continuity of solutions with respect to the initial age-distribution,hi-erarchy coefficient and harvest intensity via theoretical and numerical method.In section 3,we propose an algorithm to approximate the solutions,for which the convergence of is proved,and some numerical experiments are finished by MATLAB.The section 4 is devoted to the steady state analysis,we examine the existence of the positive equilibria,and provide some conditions from the model parameters for stability of the zero solution.The third chapter mainly concerns an extension of the model in the previous chapter:the hierarchical model with a boundary control.Section 1 describes the extended model and sets up some assumptions.Section 2 deals with the well-posedness of the model by means of fixed-point approach.In section 3,we show that the solutions to the model are continuous with respect to the control variable.In the final section 4,we present a numerical verification.