Global Exponential Stability Analysis Of BAM Neural Networks With Multiple Time-Varying Delay

Neural network is a complex network system composed of a large number of simple neurons,which can be used to solve some engineering problems,such as pattern recognition,data compression,data classification,artificial intelligence and biomedicine.These applications require neural network stability as a premise.As we all know,time delay is almost inevitable in the process of information transmission of neurons,so time-varying delay neural networks have received very wide attention.This paper proposes a new method for establishing the global exponential stability criterion of time-varying delay neural network: a direct analysis method based on system solution.The main research contents are as follows:Firstly,the p-norm global exponential stability of BAM neural networks with multiple unbounded time-varying delays is studied.In this thesis,the global exponential stability criterion is obtained directly based on the definition of global exponential stability and obtained stability criterion only requires to solve some linear scalar inequalities,which is easy to verify.Two numerical examples verify the effectiveness of the proposed method.Then,the positivity and global exponential stability of BAM neural networks with multiple time-varying transmission delays and unbounded distribution delays are studied.Firstly,we proved that the system solution is a sufficient condition for being positive.Then we prove the existence and uniqueness of the positive equilibrium point.Finally,we give the global exponential stability criteria of the BAM neural networks under consideration,and the inequalities in the criteria involve fewer decision variables,which is easy to solve.Two numerical examples verify the effectiveness of the proposed method.Finally,the positivity and global exponential stability problems of high-order Cohen–Grossberg BAM(CGBAM)neural networks with multiple proportional delays are studied.we proved that the system solution is a sufficient condition for being positive,and then derive the global exponential stability criteria based on the definition of global exponential stability.The validity of the criteria is verified by MATLAB numerical simulation.The innovation of this thesis are provided as follows:(1)A direct analysis method based on system solution is proposed,and the established stability criterion is easy to verify,which can reduce the amount of computation compared with the method of constructing Lyapunov-Krasovskii(L–K)functionals;(2)The method proposed in this thesis has good expansibility and can be applied to other analysis and design problems related to BAM neural networks with multiple time-varying delays(For example,generalized dissipation,passivity,pulse,switching,etc),and can also be extended to multiple time-delay system models(For example,leakage time-delay,constant time-delay,etc).