Existence Of Periodic Solutions For Two Classes Of Delay Differential Equation Models

In this paper,the existence of periodic solutions for two kinds of delay differential equation models is studied.One is to study the existence of periodic solutions of Cohen-Grossberg neural network models with mixed delays,in the case of discontinuous excitation functions,and establish some the new sufficient conditions that give a numerical argument The difference from the existing literature is that we consider the excitation function is discontinuous in the Cohen-Grossberg neural network model,while taking into account the infinite time lag,which undoubtedly increases the workload,but makes the theoretical results more perfect and more general.The second is that under the condition of the differential equation index n>1,some more advanced conditions are established for the existence of positive periodic solutions of the neoclassical economic growth model,and a numerical verification is given.We know that the development of this model is frustrating and far-reaching.The literature has also made good results,but most of the considered indices are n=1,or 0<n<1,which has certain limitations.This expands the scope of n and completes the existing conclusions.In the last part,we describe the background,development and prospects of two types of differential equation models.The main contents include the origin,development history and prospects of the two types of models.Finally,based on the research content of this paper,some suggestions and prospects are given.In short,the length of this paper is divided into three parts,the details are arranged as follows:In the first chapter,we consider the Cohen-Grossberg neural network model.The Cohen-Grossberg neural network model in this part not only has time-varying time lag,but also considers the case with infinite time-delay.To some extent,the model is more specific.Moreover,the excitation functions in the Cohen-Grossberg neural network model discussed by many scholars are mostly continuous.The excitation function in the Cohen-Grossberg neural network model we considered is discontinuous in this paper,and more general for practical reasons.In this paper,Mawhin's coincidence degree theorem,M-matrix theory and differential inequality techniques are used to establish new sufficient conditions to verify the existence of periodic solutions.The results of the dynamics of this model are improved and generalized.In the second chapter,we mainly study the existence of the positive periodic solution of the neoclassical economic growth model,and consider the case of the differential equation model index n>1,which is mainly obtained by the cone fixed point theory and the differential inequality technique.The sufficient conditions for the existence of positive periodic solutions of differential neoclassical growth models with time-delay,and in this part the rigorous theoretical proof process,and further use numerical examples to verify the rationality of theoretical results at the end of the chapter.Make theoretical support more credible.The theoretical results obtained in this part improve and generalize the existing literature.In the third chapter,we first review the origin of the two types of models,and further explain the development of the two models.The Cohen-Grossberg neural network model has a bumpy development,experiencing a rise,a defeat,and a strong twist.The neoclassical growth model has developed to a certain extent relatively smoothly,mainly due to the combination of the Chinese and Western economies and the growing market trend of China's economy.In addition,in this part,we also expounded the extensive application of two types of models in the field of engineering.Neural network models are widely used in artificial neural networks,such as associative memory,optimization problems,cancer cells,etc.A pivotal position.The second neoclassical growth model is born from the economy,non-economically unique,population growth,species erosion and other issues can be the subject of this model research.Through the introduction of the last part,we have proved that they are not only indispensable in the field of mathematics,but also in the field of applied engineering.At the end of the chapter,we also briefly describe the development prospects of the existence of periodic solutions for the two types of models.Figure[0]Table[0]Reference[50]...