Research On Stability Of Nonlinear Age-structured Population Models And Capital System

In recent years,the theory of differential equations in biology,economics,chemistry and many other fields are paid extensive attention.In real life,due to the influence of stochas-tic factors,such as natural disasters and technological progress,the stochastic population model and age-dependent capital system with stochastic parameter which were structured by stochastic differential equations(SDEs)could reflect the phenomenon's nature preferably.Normally,however,it is difficult to solve the true solution of the SDEs.To explore the dy-namic behavior of stochastic differential system is very necessary,especially learning the stability of the system.This paper studied the exponential stability and global stability of S-DEs under the random disturbance conditions which are Brown motion and Poisson process and gave a numerical solution of population model with polynomial approximation theory.This paper mainly discusses the following several aspects.The first chapter,defining strong solution and weak solution of differential equations,combining assumptions and Ito formula,the criterion of capital system is given in the lack of global Lipschitz condition.the conclusion of this part is proved by numerical examples.The second chapter,the exponential stability of a fuzzy stochastic single-species age-stucture model with Brown motion in a polluted environment is proved under linear growth condition and Lipschitz condition by using the Ito formula,Gronwall lemma,and lemmas about fuzzy concepts.Finally,we give a example to illustrate our exponential stability.The third chapter,based on polynomials approximation theory,we define the Shifted Legendre polynomials to approximate the function on the interval[0,A]x[0,T].Combining Shifted Legendre's differential matrices,integral matrices and Tau method,we transform nu-merical solution of the nonlinear age-structured population models problem to solve systems of nonlinear algebraic equations.The results of the numerical example shows the efficiency of the algorithms.