Dynamic Analysis And Synchronization Of Memristor-based Neural Circuits

Building neural circuits is is an important approach to explore the applications of biomimetics.It has immense potential for application in Bionics,intelligent control,robotics,computer science and neurophysiology,and so on.Usually,the memristor has some interesting properties,such as the pinched hysteresis loop current-voltage characteristic,nonlinear characteristic.Due to these characteristics,memristor is a potential candidate for building neuron circuits.Meanwhile,it is interesting to employ memristor in circuit implementation of the synapses because the memristor has nonvolatile and programmable capability.To the best of the authors' knowledge,the circuit in which the memristor neuron circuits are coupled by the memristor synapses is new.Hence,a flux-controlled memristor has been employed in circuit implementation of the FitzHugh-Nagumo model,and some FitzHugh-Nagumo circuits are coupled by means of the flux-controlled memristor synapses in this dissertation.It is interesting to employ the memristor in circuit implementation of the neuron model and the synapse because nanoscale size of memristor can reduce the final size and power consumption of the neural network.The circuit implementation will also have wide application prospect.The nervous system possesses mamy dynamic behaviors,such as chaos,bifurcation and periodic oscillation.One of the most important aspects of neuroscience research is synchronization.Discerning the chaotic synchronization of processes and events in the brain might offer the possibility of gathering deeper insight into understanding of the dynamical processes underlying the occurrence of epileptic seizures.Therefore,in this dissertation,the dynamic behaviors of the neuron circuit are analyzed in detail.Meanwhile,synchronization in coupled memristor-based neuron circuits is thoroughly studied.The dissertation focuses on chaos and chaotic synchronization in neural circuits.The two-terminal circuit element has been named the memristor because its resistance(conductance)depends on the complete past history of the memristor current(voltage)which is initial charge(flux)condition of the memristor.The effects of the parameters and initial conditions of memristor on the synchronization of neural circuits are studied in the dissertation respectively,which is the basis of actual application of these circuits.The main research contents in the dissertation are briefly described as follows:(1)Theory of memristor and neuron are described in detail.The theory includes the physical implementation and mathematic models of memristor,the features of memristor,the dynamic theory of memristor-based circuits,biological neuron and its mathematical model,the FitzHugh-Nagumo cable model,the structure of coupled neuronal network,chaotic synchronization theory,and so on.The memristor-based circuit of FitzHugh-Nagumo model is designed by employing a flux-controlled memristor.(2)The effects of memristor parameter on the synchronization and chaos of memristor-based neural circuits are thoroughly studied.The two different state equations for the memristor-based neuronal model are also derived.The details of the chaotic phenomena of the proposed neuron circuit are found with use of computer numerical simulations,i.e.,waveform diagrams,phase portraits,Lyapunov exponents and bifurcation diagram.The influences of memristor parameter on the chaotic dynamics of neuronal circuit are carefully considered.The ranges of memristor parameter are given when the stable chaotic behaviors occur.These results of numerical calculations are confirmed by circuit simulation experiments.Two different types of neural network circuits are built,one is the circuit in which two memristor-based FitzHugh-Nagumo circuits are unidirectional coupled by means of a flux-controlled memristor synapse,and the other is a ring of bidirectional coupled memristor-based FitzHugh-Nagumo circuit with the same coupling memristor synapse.The synchronization of these circuits is discussed,and synchronization mechanism is also found.Finally,the influences of the parameters of memristor synapse in chaotic complete synchronization are studied respectively.These results of theoretical analyses are confirmed by numerical simulation.(3)The effects of the initial condition of the memristor on the synchronization and chaos of memristor-based neural circuits are thoroughly studied.The Flux-Charge Analysis Method is used to investgate the bidirectional coupled neural circuits.The formulation of circuit equations in the flux-charge domain is obtained and the equations include the initial conditions of the memristors.A clear understanding of influence of the initial conditions on the synchronization of the coupled memristor neural circuits is thoroughly studied.As a result of varying the initial conditions of the memristor synapse,the details of synchronization with the parallel shift are derived theoretically by solving the nonhomogeneous error equations.The magnitude of the shift is confirmed to agree well with numerical simulation.Meanwhile,the influence of the initial flux condition of the memristor on chaos generation for individual neuron circuit is dicussed.Finally,the influence of the initial condition of the memristor synapse is considered on changing chaotic state for a neuron in the synchronous neural network.Interestingly,the chaos can be controlled by simply varying the initial condition of the coupling memristor without changing the circuit parameters and the other initial conditions.(4)The effects of the initial conditions of the memristor on dynamical behaviors of the FitzHugh-Nagumo circuit without external stimuli which is actually an van der pol oscillator are studied.The role of the initial flux conditions in relation to grazing Hopf bifurcations is theoretically and numerically analyzed.The periodic solutions of the memristor-based oscillator and a clear understanding of influence of the initial conditions on periodic solutions are presented.The ranges of initial conditions are given when Hopf bifurcations occur.The periodic solutions of the memristor-based oscillator are derived.A ring of three memristor-based van der pol oscillators mutually coupled by three inductors is build,and the oscillation modes of this coupled oscillator circuit are carefully discussed.Two different single-modes are found to be stable when the initial flux conditions meet some conditions.The numerical and circuit simulation experiments are found to be agreed with the results of theoretical analyses.