Stability And Bifurcation Of Hopfield Neural Networks Based On Memristor Synapses And Phase-change Memory Synapses

In neural networks,synapses are the main unit of transmission and interaction between neurons,acting as a bridge connecting neurons.The weight of synapses will change during the process of information transmission,and biological neuroscience calls this change synaptic plasticity.Synaptic plasticity is the basis of brain learning and memory functions.Memristor and phase-change memory are two important electronic components which can simulate the characteristics of neural synapses well.Therefore,neural networks based on memristor synapses and phase-change memory synapses become a research hotspot.It is well known that the applications of neural networks are closely related to their dynamic behaviors.For example,associative memory requires that the system equilibriums are stable,and the capacity of associative memory is determined by the number of equilibriums.Therefore,it is very necessary to study the dynamic behaviors of neural networks.This thesis studies the dynamic behaviors of neural networks based on memristor synapses and phase-change memory synapses.The main research contents are as follows:(1)A novel memristive synaptic Hopfield neural network model with time delay is proposed by using a memristor synapse to simulate the electromagnetic induced current caused by the membrane potential difference between two adjacent neurons.First,some sufficient conditions of zero bifurcation and zero-Hopf bifurcation are obtained by choosing the coupling strength of memristor and time delay as bifurcation parameters.Then,the third-order normal form of zero-Hopf bifurcation is obtained by using the central manifold theorem.By analyzing the obtained normal form,six dynamic regions are found on the plane with the coupling strength of memristor and time delay as abscissa and ordinate.There are some interesting dynamics in these areas,i.e.,the coupling strength of memristor can affect the number and dynamics of system equilibriums,time delay can contribute to both trivial equilibriums and non-trivial equilibriums losing stability and generating periodic solutions.(2)A phase-change synaptic Hopfield neural network model with time delay is constructed by using phase-change memory to simulate biological synapses.Some sufficient conditions for global asymptotic stability are obtained by constructing a suitable Lyapunov function.The results show that the global asymptotic stability of the system is not related to time delay,but to phase-change memory synapses.Then,the conditions of local stability and Hopf bifurcation of this system are obtained by selecting time delay as the bifurcation parameter.The direction of Hopf bifurcation and the stability of periodic solutions of bifurcation are studied by using the central manifold theorem and the canonical method.Finally,the correctness of the theory is verified by some numerical simulations.