Finite-Time Passivity And Synchronization Of Multi-Weight Coupled Memristive Neural Networks

As a new type of electronic component with memorizable and variable resistance and excellent characteristics such as non-volatility,nano-size,low energy consumption,and high speed,the memristor is an ideal device for simulating the synapses of neurons in the human brain.In the circuit implementation of neural networks,a new neural network,namely,the memristive neural network,is introduced by replacing the traditional resistors to mimic the synapses between biological neurons with memristors.In recent years,memristive neural networks have been applied to pseudo-random number generation,data prediction,secure communication,information storage,and image encryption.Compared with traditional neural networks,memristive neural networks are similar to the neural network model of human brain,and the above applications of memristive neural networks are closely related to their dynamical behaviors.Among the many dynamical behaviors of memristive neural networks,synchronization and passivity are particularly significant,and many scholars have studied the passivity and synchronization of memristive neural networks in recent years and obtained a large number of research results.Since neural networks are implemented by circuits,and diffusion phenomena will inevitably occur when electrons move in inhomogeneous electromagnetic fields,this paper considers the multi-weight coupled memristive neural network model with reaction-diffusion terms.Based on the existing research results,this paper further investigates the finite-time passivity and finite-time synchronization of multi-weight coupled memristive neural networks with and without reaction-diffusion terms.The main research contents and results of the paper are as follows:First,finite-time passivity and synchronization of multi-state coupled memristive neural networks are first investigated.A multi-state coupled memristive neural network model is given,and by using the Cauchy inequality and designing a new feedback controller,the network can achieve finite-time passivity and finite-time synchronization.Then,based on the multi-state couplings,a network model of the multi-derivative coupled memristive neural network is developed,and new sufficient conditions to enable this network to achieve finite-time passivity and finite-time synchronization are obtained by choosing an appropriate Lyapunov function and using matrix theories.Finally,two numerical simulation examples are used to verify the correctness as well as the validity of the above derivation results.Second,two network models of memristive reaction-diffusion neural networks with multi-state couplings and multi-spatial diffusion couplings are first developed,while inputs and outputs of different dimensions are also considered.Then,using the definition of finitetime passivity,the definition of finite-time synchronization,the Schur complement,the Wirtinger inequality and the Rayleigh-Ritz theorem,new criterion to ensure that the above two network models can achieve finite-time passivity,finite-time input strict passivity,finitetime output strict passivity and finite-time synchronization are given.Finally,the obtained theoretical results are verified numerically and simulated in images by Matlab.