Analysis And Design For Associative Memory Based On Delayed Recurrent Neural Network With Memristor

In order to process information intelligently, people set up neural network to simulatethe function of human brain. Traditionally artificial neural network has been implementedwith circuit and the connection between neural processing units is realized with resistor.Resistance is equal to strength of synapses between neurons. The strength of synapses isvariable while resistance is invariable. To simulate neural network of human brain bet-ter, this paper uses memristor as connection between neural processing units to present themodel of memristor recurrent neural network.Firstly, this paper analyzes memory property of the fourth circuit element with the in-tegration constant produced by deducing the relation of current and voltage between mem-ristor. Simulation shows that there is a threshold voltage existing, i.e., memristance cannot be changed when input voltage is less than threshold voltage. Then by replacing re-sistors with memristors, it presents the model of continuous memristor recurrent neuralnetwork(CMRNN). According to the property of memristor, CMRNN is a family of neuralnetworks in fact. By dividing the state space and contraction mapping theorem, it results thateach network in the neural networks has (2k)nstable equilibria and limit cycles where k isthe step number of step activation function and n is the number of neurons. With method ofsingular value decomposition, associative memory synthesis procedure based on CMRNNis presented.Secondly, it presents the model of discontinuous memristor recurrent neural network(DMRNN)by replacing resistors with memristors in the circuit. The discontinuous activa-tion function is a piecewise constant in the state space. The number of output constant valueis4k1，(k≥1). DMRNN is neural network series in fact. After defining the solutionin the sense of Filippov, it results that each neural network with n-neurons in the series has(4k1)nlocally exponentially stable equilibria. Next, it presents the design programm forassociative memory based on DMRNN.Thirdly, this paper prsents a family of fuzzy Cohen-Grossenberg neural network byusing memristors as the connection of Cohen-Grossenberg neural network and introducingfuzzy logic into this network. Then it discussed the existence of attractor family of suchneural network. With the method of numerical iteration, sufficient condition is given for theexistence and uniqueness of solution of such neural network. Then sufficient condition isderived for robustly asymptotically stability of neural network with the method of monotonefitting approximating. So each network has a attractor in the series, i.e., such memristor Cohen-Grossenberg neural network has a family of attractors. At last, it concludes the workof this paper and points out the work in the future.