Dynamic Behaviors Analysis For Delayed Cohen-Grossberg Type Neural Network

In recent decades, the research for nonlinear systems is becoming an important subject which internal and oversea scholars are very concerned on. As one kind of nonlinear systems, neural network has also attracted much attention because it has good performance. At present, it has been applied in some fields successfully, such as pattern recognition, image processing, and artificial intelligence, etc. Cohen-Grossberg neural network, as an up-and-coming youngster, has own particular superiority. It not only links with biological network closely, but also settles the nonlinearity and uncertainties problem that exist among the systems in practical application. So, the research and analysis of characteristic for a class of Cohen-Grossberg type neural network has also gradually become highlight in those fields that people are always concerned focus.In this paper a class of delayed Cohen-Grossberg type neural network is studied. According to the need of practical application, by using the classical theory of Lyapunov, the Linear Matrix Inequality tools and adaptive robust control methods, the Lagrange stability and finite-time boundedness of this model are investigated. At the same time, the robust adaptive convergence of the kind of network model is also discussed. Consequently, the paper will extend the study of stability for neural network at all times to wide dynamical behavior research fields. The major contributions of this dissertation are as follows:In Chapter I, the development of neural network and current advance of study on the neural network model is given. Meanwhile, the current advance of study on three different kinds of content in this paper and the significance of the paper are also introduced briefly, and the program of this dissertation is given, too.In Chapter II, the problem of the global exponential stability in Lagrange sense and global exponential attractive for Non-autonomous Cohen-Grossberg neural network with time-varying delays is studied. Making no assumptions on the number of equilibria and basing on two different kinds of activation functions, by using a new lemma and constructing appropriate Lyapunov function, some sufficient algebraic criteria are given for the global exponential stability in Lagrange sense and detailed estimation of global exponential attractive sets. In the end, an illustrate example is given to verify the results. The conclusion in this paper extends the stability conditions. The problem of finite-time boundedness for a class of Cohen-Grossberg neural networks with multiple delays and parameter perturbations is analyzed in Chapter III. By way of extending the concept of finite-time boundedness for time delay system and constructing a suitable Lyapunov function and using linear matrix inequality technique, some delay-dependent criteria are derived to guarantee fininte-time boundedness for uncertain and certain Cohen-Grossberg neural networks with multiple delays. Meanwhile, an algorithm is also presented. Finally, simulation examples are given to demonstrate the effectiveness of the conclusion.In Chapter IV, the problem of robust adaptive convergence for a class of uncertain Cohen-Grossberg neural networks with time-varying and mixed delays is investigated. Using employing a novel lemma, restricting to the uncertainty term and constructing the Lyapunov method, some delay-independent conditions are derived to ensure the state variables of the discussed mixed delays robust system to converge, globally, uniformly, exponentially to a ball in the state space with a pre-specified convergence rate. At the same time, there is no needed considering the existence and uniqueness of the equilibrium point of Cohen-Grossberg neural network. The effectiveness and usefulness of the theoretical results has been verified by numerical example with illustrations.