Memristive Electromagnetic Induction Effects On Hopfield Neural Network

Memristor,which possesses the nonlinear electrical characteristics like neuron synapse,is an ideal circuit element for mimicking synaptic plasticity.In neuroscience,the resistive weight can be replaced with the memristive synaptic weight to achieve the variable connection weight of neurons.Or the memristor can be employed to express the electromagnetic induction induced by external electromagnetic radiation or inner membrane potential of neurons for emulating the complex dynamical effects of neurons in the real electrophysiological environment.Inspired by these works,in this dissertation,we use the Hopfield neural network(HNN)as the object to study the dynamical effects of the activation gradient and the memristive electromagnetic induction.Firstly,dynamical effects of the activation gradient on HNN are studied.The response speed of neurons to external stimuli is mathematically denoted by the activation gradient value.Thus,an activation gradient HNN model is proposed thereby.Dynamically simulated tools of bifurcation diagrams,finite-time Lyapunov exponential spectra,local attraction basins,and dynamical maps are used to reveal dynamical effects including bifurcation,coexisting symmetry attractors,and so on,which are induced by the activation gradient.Furthermore,the corrections of numerical simulations are well verified by hardware experiments.Secondly,the electromagnetic induction effects of two kinds of memristors on HNN are studied,including ideal memristor and non-ideal memristor electromagnetic induction effects.Considering the HNN model possesses the standard activation gradient,electromagnetic induction flows can be induced when membrane potential differences between two interconnected neurons are existed in HNN,whose effects are equivalent to the two-way induced currents generated by a flux-controlled memristor linking two neurons.Hence,two electromagnetic induction HNN models of ideal memristor and non-ideal memristor are proposed in succession.The electromagnetic induction HNN model of the ideal memristor has the line equilibrium,whose stabilities are affected by the memristor coupling strength and initial condition.However,the electromagnetic induction HNN model of the non-ideal memristor has the decided equilibrium points.With the increase of memristor coupling strength,the number of equilibrium points adds and ones stabilities have complex evolutions.Besides,electromagnetic induction effects of two kinds of memristors,i.e.,coexistence patterns of neurons inducing by initial conditions are uncovered by multiple numerical simulation methods.And lastly,the analog circuits are developed to validate the numerical simulation results.