Memristor-based Chaotic Neural Network And Associative Memory

Since the last century,people have begun to simulate the function of the human brain,so research on artificial neural networks has been born.From the perspective of information processing,artificial neural networks abstractly process biological neurons and construct networks based on different connection methods to establish mathematical models.A highly nonlinear dynamic system composed of different neurons through specific connection rules.This system has the ability of self-adaptation,self-organization and real-time learning,which is neural network.Chaos refers to the movement that occurs in a particular system.This movement is irregular and exhibits randomness.The chaos phenomenon was observed in the brain nervous system,which aroused people's research interest.Subsequently,some people combined chaos and neural networks,resulting in neural networks also having chaotic behavior,which made neural networks closer to the brain nervous system.Therefore,chaotic neural networks are considered as a new generation of information processing technology,and have attracted researchers' interest in many fields such as image processing,pattern recognition,and combination optimization.Memristor is a nano-sized,low-power synapse-like device.Designing new synaptic circuits and applying them to the representation of synaptic weights in neural networks lays a solid foundation for future hardware implementation of neural networks.Firstly,this paper analyzes two memristor models,titanium dioxide memristor and spin memristor.Their formulas for resistance change were deduced through formulas,and numerical simulation experiments were performed with matlab to observe the changes in resistance values.The resistance of titanium dioxide memristors changed linearly with time.In order to solve the problem that the boundary migration rate of the titanium dioxide memristor is constant,we introduce a non-linear window function,and derive the relationship between the resistance and charge of the memristor by adding the Joglekan window function through the formula.Through matlab simulation,After adding the Joglekan window function,the resistance values of titanium dioxide memristors and spin memristors are non-linear with time.It includes a single memristor as a synapse,a bridge synapse circuit composed of4 memristors and a bridge synapse circuit composed of 2 resistors and 2 memristors.We have given their circuit structure diagram.We analyze the resistance change and synaptic weight change of the memristor in the circuit by formula,and then use matlab to carry out simulation experiments to verify our analysis results.Single memristor synapses can achieve positive synaptic weights,the other two can achieve positive,negative,and zero synaptic weights,and then summarize the advantages and disadvantages of three memristor-based synaptic circuits.This laid the foundation for our subsequent synaptic circuit design.Then,we added threshold constraints and window functions to the titanium dioxide memristor,and used it to design a new memristive synaptic circuit.We analyzed its synaptic weight changes,which can achieve-1 to 1 Weight changes.Based on this memristive synapse circuit,we designed a weight sum circuit.This memristive synapse circuit can be used to represent the connection weights between chaotic neurons in a chaotic neural network,and the weight sum circuit can represent the accumulation of connection weights.Then we based on this memristive chaotic neural network design simulation experiment to realize self-associative memory,separation of superimposed patterns,hetero-associative memory,many-to-many associative memory and the application of three views.Finally,we analyzed the dynamic behavior of chaotic neurons and chaotic neural networks.By observing the bifurcation diagram,the average time firing rate and the Lyapunov exponent of the chaotic neural network with the change of the refractory parameters and the maximum Lyapunov exponent of the chaotic neural network.In the case of other parameters unchanged,the refractory parameters control the chaotic state of chaotic neuron and chaotic neural network.