Chaotic Dynamics Research And Circuit Implementation Of Memristive Nerural Networks

Building neural network models is an important way for brain-like research,and its development will greatly promote the development of artificial intelligence fields such as big data,cloud computing,deep lear ning,intelligent robots,and so on.Based on the neural network models,analyzing and researching its dynamics,exploring and revealing the working mechanism of the brain from the computational level,has important theoretical and practical significance f or computational neuroscience and the development of intelligent artificial neural networks.However,traditional neural network models use resistors with fixed resistance to simulate synapses with variable strength,and can not generate complex brain-like chaotic characteristics.This has become the main restrictive factor in artificial neural network brain-like research.Memristor which is a basic circuit element with variable resistance has synapse-like biological characteristics such as programmability,memory,and nonlinearity.Therefore,the memristor-based synapse can be used to replace the resistor-based synapse in the traditional neural network models to construct memristive neural network models.Besides,due to the magnetic flux characteristic of the memristor,the memristor can be used to describe the magnetic induction effect of neurons affected by electromagnetic radiation,so as to establish a model of neural networks under electromagnetic radiation.Compared with the traditional neural network models,memristor-based neural networks have richer dynamical characteristics,especially can produce complex brain-like chaotic behavior,and can more truly reflect the complex dynamical features of the biological nervous systems.Thus,in this article,the chaotic dynamics of memristive neural networks is investigated detailedly.And some work in the mathematical modeling of memristive neural networks,chaotic dynamics analysis,and circuit implementation is done.The specific content and innovations can be summarized as follows.(1)A three-stable locally active memristor model is proposed,and a locally active memristive HR neuron model is constructed.The firing dynamics of the locally active memristive neuron is investigated by using various numerical anal ysis methods including equilibrium point analysis,bifurcation diagrams,Lyapunov exponent spectrum,time sequences,phase plots,and so on.Theoretical and numerical analysis show that the locally active memristive neuron can not only generate periodic sp iking and bursting,stochastic spiking and bursting,as well as chaotic spiking and bursting,but also exhibit complex dynamical behavior of firing multistability.Compared with the traditional neuron models,the proposed memristive neuron model has obviou s characteristics of chaotic firing and multistability.Furthermore,a chaotic circuit of the memristive HR neuron is designed,and the numerical simulation results are verified by hardware experimental results.(2)A multi-stable memristor model is proposed,and a multi-stable memristive Hopfield neural network model is established.The chaotic dynamics of the multi-stable memristive Hopfield neural network is studied by using bifurcation diagrams,Lyapunov exponents,phase plots,basins of attraction,and so on.Research results show that the multi-stable memristive Hopfield neural network can not only produce rich chaotic behavior but also generate coexisting infinite chaotic attractors with the same topology but different positions.So,the proposed memristive neural network has the characteristics of complex extreme multistability.Different from the traditional neural networks,the presented multi-stable memristive neural network is very easy to generate chaos and has obvious multistability.Finally,the chaotic circuit of the memristive neural network is designed and implemented in the PSIM circuit simulation tool.The numerical results are confirmed using circuit simulation results.(3)Using magnetic controlled memristor to describe the magnetic induction effect of the neuron under electromagnetic radiation,a Hopfield neural network under electromagnetic radiation is presented.The influence of electromagnetic radiation distribution on the chaotic dynamics of the neural network is researched by adjusting the system parameters to change the distribution of electromagnetic radiation on the neural network.The results show that for the Hopfield neural network with three neurons,as the number of neurons stimulated by electromagnetic radiation increa ses,the dynamical behaviors of the neural network can be gradually changed from periodic oscillation to chaos,transient chaos,and complex hyperchaos.By adjusting the distribution of electromagnetic radiation,the dynamical state of the neural network can be changed,which provides a new idea for the prevention and treatment of neurological diseases.Finally,the chaotic circuit of the neural network under electromagnetic radiation is realized,and the numerical simulation results are demonstrated via hardware experiments.(4)Using magnetic controlled memristor to describe the effect of magnetic induction and utilizing multi-level logic pulses to realize current stimulation,a Hopfield neural network with different external stimuli is proposed.By adopting equilibrium point analysis,bifurcation diagrams,Poincare maps,basins of attraction,the chaotic dynamics of the proposed neural network is revealed under three different cases including no external stimulation,only electromagnetic radiation stimula tion,as well as electromagnetic radiation and multi-level logic pulse simultaneous stimulations.Research results show that with the increase of the type and complexity of the external stimuli,the dynamical behavior of the neural network is transformed from periodic attractors to chaotic attractors,double-scroll attractors,four-scroll attractors,and six-scroll attractors.Moreover,Hamilton energy analysis shows that the energy of the neural network mainly depends on its dynamical state,rather than external stimuli.Finally,the chaotic circuit of the neural network under the three conditions is realized,and the numerical results are verified by hardware experiments.