Almost Periodicity Of Several Kinds Of Differential Equations

One of important question of delay differential equations is to study the qualitative property of the solution, such as stability,periodic solution,almost periodic solution and so on. Almost periodic solution has always been an important branch of the differential equations and has a very important significance in theory and practical application. This paper mainly studies the existence and stability of the almost solutions for two kinds of multi-species logarithmic population models and a kind of competitive neural networks with different time scales. This paper has five chaptersChapter 1 introduces the present situation of almost periodic solutions for differentiable dynamical system, the current status and meaning of almost periodic solutions for multi-species logarithmic population model and competitive neural networks with different time scales, while introducing the main contents and originalities of this paper.In Chapter 2, bases on Banach fixed-point theory and the technique of differential inequality, the essay explores a class of multi-species logarithmic population model with feedback control, and establishes the novel criteria on the existence,uniqueness and global attractivity of almost periodic solution. The outcomes of the chapter relax the constraints on the delays are differentiable and the boundedness of the integral of interrelated parameter in the related literature.Chapter 3 discusses a neutral multi-species logarithmic population model, by employing Banach fixed-point theory,exponential dichotomy theory and the technique of differential inequality, the novel sufficient criteria are established on the existence,uniqueness and global exponential stability of almost periodic solution. Furthermore, the outcomes in this chapter remove the restriction on the delays are constants and the coefficients of neutral term are differentiable, the conclusions of the chapter improve the conclusions drawn from the existing literatures. This method can be also applied to the multi-species logarithmic population model without neutral terms.Chapter 4 proposes a kind of neutral competitive neural networks with different time scales, by employing Banach fixed-point theory and the technique of differential inequality, the novel sufficient criteria are established on the existence,uniqueness and global exponential stability of almost periodic solution without requiring the activation function to satisfy global Lipschitz condition. The conclusions of the chapter include or improve the conclusions drawn from the existing literatures.Chapter 5 concludes the research work of this paper, and looks forward to the future research directions.