Research On Multistability Of Recurrent Neural Networks

Neural network has been one of the focuses of artificial intelligence,and has achieved fruitful results in the past few decades.The dynamic behavior of neural network is a prerequisite for application and design,which is widely used in image processing,pattern recognition,optimization problems and other fields.Compared with the monostable study,the multistability and robustness of neural networks show the complex dynamic behavior.Therefore,it is of great significance to study the multistability and robustness of neural networks to improve the theory of neural networks,and to expand the application of neural networks in artificial intelligence.By using fixed point theory,topological degree theory,nonsmooth analysis,right discontinuous differential equation filippov theory,the multistability of neural networks with time delays is analyzed.The main research contents of this dissertation are presented as follows.The multistability of recurrent neural networks with saturated activation function is discussed.By using Banach's fixed point theorem and Brouwer's fixed point theorem,some sufficient conditions for the existence of(4k + 3)n equilibrium points are given in recurrent neural networks.and(2k + 2)n equilibrium points are proved to be locally exponentially stable,where k is a positive integer.The multiple Lagrange stability under perturbation is studied.By constructing sets of coupled partitions and using the generalized M-matrix,the local asymptotic stability of equilibrium point is discussed.By using the delayed differential inequality,the Lagrange stability of the error trajectory of the perturbed neural network is presented.The ?-type stability of Cohen-Grossberg neural networks with unbounded delay is studied.According to the geometric features of activation functions,the appropriate parameters and dynamic regions are selected,and the dynamic division of the state space is given.Considering the relationship between equilibrium and topological degree,the invariance of algebraic sum of equilibrium points is proved for Cohen-Grossberg neural networks with smooth perturbation.Compared with the relevant results,the conclusions are relatively new and the obtained conditions have good compatibility,which extends the previous results to some extent.The multiple ?-type stability and robustness of recurrent neural networks with discontinuous activations are discussed.Based on the Filippov theory of the differential equations with discontinuous right-hand sides,by using the analysis method?the inequality technique and taking appropriate parameters,sufficient conditions and algebraic criteria of ?-type stability and robustness are obtained for recurrent neural networks with discontinuous activations.Compared with some related results,the results of these dynamic behaviors complement and enrich the previous results,which is helpful to the design of associative memory of neural networks.Finally,a conclusion for all discussions is given in the dissertation.The future research on multistability is prospected.