The Study Of Dynamical Behaviors Of A Class Of Diffusive Circadian Rhythm Model

In this paper,according to the circadian rhythm phenomenon occurring in nature,the physiological,biochemical and behavioral oscillations of the organism occur in a 24-hour cycle,a kind of reacfion-diffusion circadian rhythm model with and without time delay is considered as the research object.The global existence,boundedness,the long time asymptotic behaviors of the solutions and the existence of the bifurcation periodic solution for the reaction-diffusion circadian rhythm model are studied by using the fundamental theory of Partial Differential Equations of both parabolic and elliptic types,as well as the bifurcation theory of the infinite-dimensional dynamical systems.The specific contents are as follows:In chapter 1,we introduce the research background,the domestic and international research status and the main research work in this paper respectively.In chapter 2,we investigate the global existence,boundedness,the existence of the attraction region,and the long time asymptotic behavior of the solution for the reactiondiffusion circadian rhythm model without time delay.In particular,we give the conditions that the solution of the Turing mode does not exist.In chapter 3,we consider the asymptotic behavior of the Circadian Rhythm Model and the diffusive Circadian Rhythm Model with time delay and the specific properties of Hopf bifurcation.The theoretical results obtained in this paper can allow for clearer understanding the inner principle of the generation of the circadian rhythm problem mode more clearly.The corresponding mathematical work can provide the theoretical reference for the numerical work of the scientists in applied sciences.