Investigation Of Dynamics In Memristor-coupled Oscillators And Network

With the rapid development of the information technology,information storage,nonlinear circuit and artificial neural network have aroused great concern.Memristor is a kind of nonlinear circuit component with memory effect.Its appearance has great significance for the design of integrated circuits.Memristors can be used to reduce the size of integrated circuits,and improve the nonlinear characteristics of chaotic circuits.Moreover,the unique memory characteristics of memristors can describe the memory function of neuronal synapses,which have a breakthrough effect on brain scientific development.In this paper,the resonant circuit of the memristor coupled Josephson junction and the neuron model coupled by the memristor are constructed.The dynamics and applications of the memristor coupled system are studied by using the common methods in nonlinear dynamics and statistical physics.The detailed research contents and results are as follows:(1)The resonant circuit of the memristor coupled Josephson junction is built.Considering the electromagnetic induction effect,the induced current term across the memristor is added to the circuit equation,which improves the nonlinear characteristics of the circuit.Based on the nonlinear dynamics theory and numerical simulation,the dynamic behavior of this system is studied.It is found that the output signal of the system can be switched between chaotic state and periodic state by adjusting the induced current intensity.Further,the chaotic signal generated by this system effectively realizes the encryption protection of information,which enhances the security of data communication.(2)Based on the memristor coupled Josephson junction circuit,a two-dimensional regular network is constructed to study the change of the topological connection and local abnormality in the network affected the evolution and stability of the spatial pattern with using the pattern theory and synchronization theory.Additionally,considering the influence of noise on the pattern in the network,the synchronization factor,correlation function and signal-to-noise ratio are calculated to analyze the effect of Gaussian white noise on the stability of the pattern in the network.(3)A neuron model of memristive autapse was constructed,and the memristive autapse current is introduced by memristor,which realizes the autaptic memory function.The effect of memristive autapse current on the firing pattern of neurons is discussed by observing the membrane potential time series and bifurcation diagram.Meanwhile,the evolution of pattern is studied in the memristive synaptic-coupled chain-like neuron network,and the synchronization of the network can be suppressed by adjusting the memristive synaptic current.(4)A neural network model containing memristive autapses is proposed based on memristor.Considering the electromagnetic induction effect in nerve cells,the effects of memristive autapse on the formation and evolution of patterns in neuronal networks were studied.The transition of spiral wave and target wave in the network can be realized under the appropriate memristive autapstic current intensity.Finally,It is discussed that the external electromagnetic radiation affects the evolution of spiral waves in neural networks.In summary,based on the chaos theory,the statistical physics,and the pattern theory,we studied the nonlinear dynamic behavior of the memristor coupled system and the evolution of spatiotemporal patterns in regular networks,which are constructed by the improved model in this paper.This is a theoretical significance for exploring the application of memristor in chaotic circuits and neural networks.