Dynamics Of High-order Fuzzy Cellular Neural Networks

Since the high-order fuzzy cellular neural networks (HFCNNs) have strongerapproximation property, faster convergence rate, great stronger capacity and higher faulttolerance than ordinary fuzzy neural networks, more and more scholars actively investigate thehigh-order fuzzy neural networks, and the results obtained have been more widely used inpattern recognition, associative memory and optimal combination. Applications rely heavily onthe dynamic behavior of the neural network, such as stability, synchronization, convergence,fault-tolerant, oscillation and so on. It’s more significant to study the dynamics of high-orderfuzzy neural cellular networks. In this thesis, the stability and the exponential periodicity ofHFCNNs with time-varying are investigated.In chapter one, the development process and the basic theory of HFCNNs are introduced,and the background and significance of HFCNNs are highlighted. In addition, the innovation andmeaning of this study are illuminated. In chapter two, the existence, uniqueness and exponentialstability of equilibrium point and uniform boundedness for this system are studied based on theexisting research results. Some sufficient conditions of stability are derived by using Brouwer’sfixed point and employing analysis technique. In chapter three, global exponential periodicityand stability of HFCNNs with time-varying delays are investigated. By constructing suitableLyapunov function and applying the Brouwer contraction mapping principle, the existenceuniqueness and global exponential periodicity are obtained. An example is given to illustrate theeffectiveness of the obtained results. In chapter four, the dynamic behavior of high-order fuzzycellular neural networks with time varying coefficients and delays are considered. Somesufficient conditions are derived for the exponential convergence of such HFCNNs withoutrequiring the Lipschitz continuity condition. In the last chapter, the research of this paper issummarized and the future developing directions are included.