Bifurcation And Stability Analysis Of Annular Delayed Cellular Neural Networks With Self-connection

This thesis analyzes the Hopf bifurcation and stability of annular delayed neural networks with self-connection, by applying the center manifold theorem and the normal form theory, in which the center manifold theorem is applied to reducing dimensions, while the normal form theory for simplifying the form of our models.In Chapter 1, we briefly introduce the background and the recent development of the issue we researched , in which its applying and the purpose of the investigation are denoted, too.In Chapter 2, we discuss the stability and bifurcation of an annular delayed neural network with self-connection:We obtaine some relevant results, and then make the numerical simulation experimentsto verify them.In Chapter 3, we investigate the stability and bifurcation for a class of threeneuronnetwork with two delay and self-feedback:We obtaine some relevant results, and then make the numerical simulation experimentsto verify them.In Chapters 2 and 3, each chapter consists of three parts, the first part is for the introduction and model ; the second part mainly analyzes the linear stability of trivial solution, gives some sufficient conditionsstability and instability ,discusses the existence of a branch and gives the formula for calculating the value of branch through regarding the self-feedback delay as the parameter of branch ; the third part uses the center manifold theorem and the normal form theory to determine the branch direction and stability of periodic solutions nature, and gives examples of numerical simulation experiments to verify the main results of this paper.