On The Dynamics Of A Class High-order Fuzzy Cellular Neural Networks

Since neural networks have enormous potential in wide varieties of appli-cations, many specialists and scholars apply themselves to the research of thetheory and achieve many perfect productions. In this paper, we perform re-searches of the stability and existence of periodic solution of high-order fuzzycellular neural networks (HFCNNs). The main contents of this paper include:existence of periodic solution and the stability analysis for a class of HFCNNswith constant and time-varying delays , respectively.The main contents in this paper can be summarized as follows:1. Firstly, in the first subsection of the first section, we give a simple in-troduction of neural networks. In the following subsection 2 we introduce thedevelopmental process and significance of fuzzy cellular neural networks. In sub-section 3, we introduce the research results for fuzzy cellular neural networks. Insection 4, the research contents of this paper is given.2. In the second section, we mainly analyze a class of high-order fuzzycellular neural networks with constant delays. Firstly, we analyzed the existenceuniqueness and global exponential stability of equilibrium point, by assumingthat the input and bias are constants. We obtain the existence uniqueness ofequilibrium point, by Brouwer fixed theorem and obtain the global exponentialstability by using LMI and Lyapunov functional method. Secondly, we obtainthe existence uniqueness and global exponential stability of periodic solutions byassuming that the input and bias are periodic continuous functions.3. In the third section, we mainly analyze a class of high-order fuzzy cel-lular neural networks with time-varying delays. Firstly, we proved the existence uniqueness and global exponential of equilibrium point, by topology degree theo-rem. But, for stability, we found that it is di?cult to give proof, by LMI method.Hence, we use nonsingular M-matrix method, then, the proof become easy.4. In the forth section, we analyze a class of high-order fuzzy cellular neuralnetworks with time-varying delays by using p norm. We get the global exponen-tial stability of equilibrium point of system, by using an important inequality—Young inequality.