Multistability Of Fuzzy Neural Networks

In the study of traditional neural network, all need to have the exact mathematical model,but in real life, there are some uncertain factors which is difficult to describe with accurate mathematical model.Therefore, the study of both uncertain fuzzy neural network information processing ability and knowledge storage ability of two kinds of technology is of great significance.The superiority of the fuzzy neural network is reflected in the processing of nonlinear, fuzzy and other issues, especially in intelligent information processing, there is still a lot of room for development.In this paper, some simple conditions are obtained to guarantee that the n ‐ dimensional fuzzy neural network can have not more then 3nequilibrium points by used the method of the compression mapping principle and interval segmentation. These conditions can be developed from the improvement and extension of the existed ones. The validity of theoretical results are showed in one illustrative example.Chapter 1 is introduction,it mainly includes the development history of the fuzzy neural network, the background and the brief introduction of the content of the research and some basic definitions and the lemma.In the second chapter,the isolated equilibrium points of fuzzy neural networks are discussed by using the compression mapping principle and the translation equilibrium point.In certain conditions,there are 3nsolated equilibrium points,among them, there has 2nequilibrium points are locally exponentially stable.Compared with the two methods, the latter conditions are less conservative and can be easily applied to practical problems.In the third chapter, the stability of the fuzzy neural network with Mexican‐hat‐type excitation function is studied.It have shown that the n‐dimensional fuzzy neural network can have2#3Nequilibrium points and have2#2Nequilibrium points which are locally stable.The last part is the conclusion and prospect.on the one hand, the part made a brief summary of the full text. on the other hand,it can give some further research direction.