Research On Synchronization Control Of Field Coupled Neurons With Time Delay

In nervous system,information transmission and transformation between neurons are achieved through synapses mainly,and synaptic function depends on the synergistic interaction between electrical and chemical synapses.However,the nervous system has inherent time delays due to the limited propagation speed of neuronal impulses along axons and the lag caused by synaptic processing.In addition,chemical synaptic coupling,which is described by embedding an induction coil into the coupling channel equivalently,may be the most suitable way to achieve synchronous information encoding between neurons,compared with electrical synaptic coupling.Because continuous pumping of ions can induce magnetic fields in cells,and all neurons are controlled by effective field energy pumping completely.Therefore,we believe that field coupling may provide another effective way to realize signal transmission and information encoding.The main research contents of this thesis are as follows:1.Two HR neurons are coupled via an induction coil to excite a magnetic field.During the coupling process,there must be a time delay in the transmission of information,so the time delay is introduced into the coupled model.First,the firing characteristics and bifurcation modes of two identical HR neurons are studied by using the bifurcations of one-parameter and two-parameter.It is found that chaotic and high-period states disappear,and the bifurcation modes become simple with increasing the time delay and coupling strength.Then,the possible synchronization patterns of two HR neurons with different stimulation are analyzed by error diagrams and time series diagrams.It is confirmed that the synchronous firing patterns are not only associated with neurons with high stimulation current,but also with time delay and coupling strength,and with some regularity.2.Based on the first part,the coexisting firing activities and synchronization behaviors in the dual neuron network which depend on the external stimulation current,coupling strength,time delay and initial conditions are simulated,respectively.Then the infinite number of firing modes including chaotic firing,periodical firing,and quiescent state is induced by initial conditions.It also shows the types of synchronization related to the initial value,including complete synchronization,delayed synchronization and asynchronization,and the state of complete synchronization exhibits only quiescent state and period-1 firing when the time delay is not equal to 0.Furthermore,the linear augmentation method is conceived to control extreme multistability.It can be found that the attractors with different positions and topological structures can be controlled to the point attractors with the same shape but with different positions when the coupling strength of linear system and nonlinear system is increased.That is,the heterogeneous multistability can be successfully controlled to the homogeneous multistability,and the coupled neurons can also be achieved complete synchronization after control.3.Resistor and inductor are employed to connect two HR neurons in order to describe the coupling effects of electrical synaptic and chemical synaptic in the actual neuronal network,respectively.Moreover,distributed time delays are introduced into the coupling terms when taking into account that the propagation of neuronal signal is non-instantaneous and non-uniform.For the resistor-coupled and inductor-coupled neuron models containing weak and strong kernel functions,the effects of synaptic coupling enhance on synchronization behavior and the bifurcation structures are compared among the three control modes(without control,using Lyapunov control and using back-stepping control).Then complete synchronization and approximate synchronization behaviors are revealed,and it is confirmed that the implementation of synchronization and bifurcation patterns of coupled neurons depend on the selections of coupling channels and kernel functions.Finally,the optimal control method is back-stepping control method by comparing from three aspects of controller design,synchronization error and synchronization range.