Research On Modeling And Application Of Fractional Order Memristor Neural Networks

Memristor is a new type of electronic component,which has the characteristics of nonlinearity,memory,adaptability and synaptic like,and is widely used in artificial neural networks and other fields.Compared with integer order calculus,fractional order calculus can more accurately describe systems with complex properties.This article constructs two fractional order memristor artificial neural network models,analyzes their dynamic behavior through methods such as time series diagram,phase diagram,and bifurcation diagram,and obtains the equivalent circuit of the fractional order neural network using time-frequency domain method.Through circuit simulation,the correctness of the theoretical analysis is further verified.The main work content of the paper is as follows:First,a new hyperbolic tangent memristor model is improved,and the v-i characteristics of the hyperbolic tangent memristor port are analyzed by applying different voltage excitations to it.It is verified that it meets the three basic characteristics of memristor and is a generalized memristor.The numerical simulation results were verified through circuit simulation based on the Multisim platform.Secondly,based on the concept of Hopfield neural network,a fractional order memristor based Hopfield neural network(FOMHNN)is constructed.This neural network has three neurons,and uses memristor to replace the synaptic weights connected between neurons.Adomian decomposition method is used to simulate the phase diagram,equilibrium point,stability and bifurcation diagram of the system,and analyze the bifurcation behavior under parameter changes and the coexistence attractor induced by different initial values.Establish a FOMHNN model using the time-frequency domain method to construct a fractional order capacitance equivalent model.Circuit simulation analysis was conducted on the Multisim circuit simulation platform to verify the dynamic behavior of fractional order systems under different conditions.FOMHNN was applied to the image encryption scheme and security analysis was conducted on this confidentiality method.Verified that FOMHNN has sufficient security when applied to image encryption.Finally,the fractional order hyperbolic tangent memristor is combined with the cellular neural network to build a fractional order memristor based cellular neural network(FOMCNN).By combining dynamic analysis methods such as phase diagrams,equilibrium points and characteristic roots,and bifurcation diagrams,the effects of different parameters on its dynamic characteristics were studied.FOMCNN was applied to digital watermarking and its feasibility was verified by analyzing the performance indicators of digital watermarking.