Global Stability And Multistability Analysis Of Delayed Complex-valued Neural Networks

In recent years,with the great heat of deep learning and artificial intelligence,the upsurge of investigation of neural network has swept the world.The existence and stability of the equilibrium point of the neural network is the premise of the hardware design.Moreover,in different applications,the number of equilibrium points is different.Therefore,analyzing the global stability and local stability of the equilibrium point of neural network has become a hot topic.Compared with the existing literature about stability of neural networks,the main contributions of this paper can be summarized as follows:(1)In chapter 2,the global asymptotic stability of a complex-valued bidirectional associative memory(BAM)neutral neural network with time-delay has been studied.By virtue of homeomorphism theory,inequality techniques and Lyapunov functional,a set of delay-independent sufficient conditions is established for assuring the existence,uniqueness and global asymptotic stability of an equilibrium point of the considered complex-valued BAM neutral-type neural network model.The assumption on boundedness of the activation functions is not required,and the LMI-based criteria are easy to be checked and executed in practice.(2)Chapter 3 is concerned with the problem of coexistence and dynamical behaviors of multiple equilibrium points for complex-valued competitive neural networks with discontinuous non-monotonic piecewise nonlinear activation functions.Without assuming the linearity or monotonicity of the activation functions,by virtue of the fixed point theorem and other analytical tools,several new sufficient conditions are developed to guarantee that the discontinuous complex-valued competitive neural networks have at least 16~n equilibrium points,among which 9~n are locally stable.In addition,some criteria for assuring the coexistence and local stability of multiple equilibria for real-valued competitive neural networks are established,which also show that the number of stable equilibria for the complex-valued neural networks is larger than the real-valued ones.(3)Chapter 4 concentrates on the coexistence and dynamical behaviors of multiple equilibrium points for a class of memristor-based complex-valued neural networks(MCVNNs)with non-monotonic piecewise nonlinear activation functions and unbounded time-varying delays.Based on the geometrical configuration of activation functions,by utilizing the Intermediate Value Theorem and other analytical tools,some novel algebraic criteria are proposed to guarantee the coexistence of 25~n equilibrium points in which 9~n equilibrium points are locally?-stable for such MCVNNs.As a direct application of these results,some criteria that assure the multiple exponential stability,multiple power stability,multiple log-stability and multiple log-log-stability are established.The proposed results show that the complex-valued neural networks introduced in this paper can have greater storage capacity than the real-valued ones.Finally,for the above results,we give some corresponding examples with simulation to show the applicability and effectiveness of the obtained theoretical findings,respectively.