Passivity Analysis For Memristor-based Complex-valued Neural Networks

At present,neural networks have become an indispensable and important part of artificial intelligence research.With the continuous deepening of research,as an extension of real-valued neural networks,complex-valued neural networks have richer dynamic behaviors,so about complex-valued neural networks dynamics research has been carried out in various fields.In addition,in neural networks,passivity means that the rate of external energy supply should not be less than the internal storage rate of the system.The theoretical key is that it can keep the internal stability of the system.Passivity theory is the main tool to study the dynamic behavior of nonlinear systems(especially high-order systems).The inertia term in neural networks refers to the second derivative of the system state vector,which is equivalent to the inductance in the circuit system.This paper introduces the inertial term into the complex-valued neural network and analyzes the passiveness of the system.The two types of neural network models studied are: memristor-based complex-valued inertial neural networks with discrete and distributed delays and memristive-based complex-valued impulse inertial neural networks with time-varying delays.This paper separates complex-valued neural networks into real and imaginary parts for research.The main results of this paper are as follows:Fiirstly,Chapter 2 concentrates on the passivity analysis for memristor-based complex-valued inertial neural networks with discrete and distributed delays.The second-order derivative of the state vector is converted into the first-order derivative through appropriate variable transformations.By utilizing the theory of differential inclusions,set-valued mapping,linear matrix inequality(LMI)techniques and matrix analysis technique,some novel passivity sufficient conditions are obtained.In addition,in order to avoid the NP-hard problem with the increase of the number of network nodes,the optimal condition of the passivity is given by using the appropriate matrix analysis technique.It is worth noting that when the input term of the system is zero,the criteria in this chapter can be directly used to obtain the global asymptotic stability conditions for equilibrium of the system.Secondly,on the basis of Chapter 2,chapter 3 considers the memristor-based complex-valued impulsive inertial neural network with time-varying delays.By constructing appropriate Lyapunov functional,using inequality technique and matrix analysis technique,some novel sufficient conditions are obtained.Similarly,when the input term is zero,the global asymptotic stability condition for equilibrium of the system can be directly derived from the conclusions obtained in this chapter.Therefore,the passivity of the neural network can be regarded as an extension of stability.Finally,some simulation examples are given to verify the effectiveness of the results.