Dynamic Analysis Of Some Kinds Of Almost Periodic Delay Differential Equation Models

With the development of science and technology,more and more widely applied in various fields,especially in population ecology,infectious diseases and neural network.As a result of the existence of time delay phenomenon,the changing rule of the manythings not only depend on the state at that time,but also to the state of the past,so practical problems with delay differential equations describe the model more realistic.Through using the theory of delay differential equations,Lyapunov functional method,fixed point theorem and inequality technique,this dissertation studies the dynamic behaviors of differential neoclassical growth model with delay,gene regulatory network model with delay,and BAM neural network model with delay,which mainly include the existence of almost periodic solutions,the exponential attractivity and global exponential stability.Meanwhile,the influence of time delay on the dynamic behavior is analyzed,and the conclusions obtained in this paper complement and improve some known results.The length of this paper is divided into six parts,the details are arranged as follows:In the first chapter,the background and current situation of this paper are briefly reviewed,and the specific work of this paper is briefly summarized.At the same time,the specific application direction and learning motivation of this paper are also briefly described,then put forward the structure arrangement and main content of this paper.In the second chapter,some basic knowledge and definitions as well as some basic lemma and methods are given.In the third chapter,this chapter investigates a delayed coupled almost periodic differential neoclassical growth system,by using the theory of dichotomy and differential inequality technique,a new set of sufficient condition is derived to guarantee the existence and exponential attractivity of almost periodic solutions for the addressed system.Finally,an example is given to exhibit the efficiency of the theoretical results.In the fourth chapter,this chapter studied a class of genetic regulatory networks with time-varying delays,new criteria for the existence and global exponential stability of almost positive periodic solutions are established by using the theory of dichotomy and contraction mapping principle.An example is given to numerically demonstrate the theoretical results.The obtained results are essentially new and complement previously known result.In the fifth chapter,this chapter without using the traditional reduced order approach,we studied the exponential stability problem for a general delayed inertial BAM neural networks.New conditions are established by constructing a novel Lyapunov-Kraiiovskii functional.Finally,numerical simulation proves that the theoretical results are effective and feasible.It is worth mentioning that the proposed non-reduced order method in this paper can be generalized to inertial complex-valued neural networks,the comparison of the corresponding results in some related literatures shows the effectiveness and superiority of our method.In the sixth chapter,gives a summary of the thesis work and prospects to the further research fields.Figure[3]Table[0]Reference[90]...