Stability Analysis Of High-order Neural Networks With Proportional Time Delay

In systems such as physics,biology and Internet control,the existence of delay is unavoidable.Therefore,in order to get the stability condition of the system,the delay must also be taken into account.This paper studies the stability of high-order neural network with proportional delay,through system transformation,constructing Lyapunov function,etc.,has successively get the asymptotic stability criteria and the global exponential stability criteria of the target neural network system.Firstly,by constructing a appropriate Lyapunov function and transforming the original system,we get the stability criteria of high-order neural networks with proportional delay.The global exponential stability criteria for a constant-delay system with unbounded time-varying coefficients is first given,and then the relationship of stability between the current system and the original one is proven,so that the asymptotic stability criteria of the original system is obtained.The effectiveness of the proposed method is verified by numerical examples.Secondly,the global exponential stability criteria for high-order neural networks with proportional delays is obtained.The original network model is first transformed into a constant-delay system with unbounded time-varying coefficients,then it is proven that the global exponential stability of the original model is equivalent to the global hyper-exponential stability of the transformed system.The global hyperexponential stability criteria of the transformed system is given by constructing the Lyapunov function,applying the Halanay inequality,etc.Thereby,the global exponential stability criteria of the original system is obtained.The validity of the theoretical results is verified by numerical examples.It should be emphasized that the method proposed in this thesis can also be applied to(high-order)neural networks with multiple proportional delays.