两个非耦合Hindmarsh-Rose神经元同步的非线性特征研究

利用Hindmarsh-Rose(HR)神经元输出的膜电压作为刺激调整两个具有不同初始条件的非耦合HR神经元的电流输入，通过分析神经元放电峰峰间期(ISI)的分布揭示了两个神经元同步过程轨道演化的机理.在周期信号刺激下，两个具有相同参数原处于混沌状态的神经元可以 实现完全同步，且可以同步到不同于刺激信号频率的周期响应上；两个具有不同参数的神经 元可以实现相位同步，参数差别较小的两个神经元可以相位同步到与刺激信号不同频率的周 期响应上，参数差别较大的两个神经元只可能相位同步到与刺激信号相同频率的周期响应上 .混沌信号刺激两个神经元只可能同步到产生混沌信号神经元的放电模式上，可见混沌刺激 更有利于神经元信息编码与解码.分析两个被调整神经元系统的最大条件Lyapunov 指数(Lmc )与刺激强度k的关系表明当k达到某一阈值时两个系统的Lmc均为负值是两个系统实现同 步的必要条件.平均发放率相同的混沌刺激和周期刺激相比较混沌刺激更容易使两个神经元 实现同步，表明混沌刺激产生的效应更强，该结论与实验结果相符合. 关键词： 放电峰峰间期 同步 相位同步 条件Lyapunov 指数

Study on nonlinear characteristics of two synchronizing uncoupled Hindmarsh-Rose neurons

Modulating the current input of two uncoupled Hindmarsh-Rose neurons by using the membrane potential of Hindmarsh-Rose neuron under different initial conditions, the evolution mechanism of synchronization process of the two neurons is revealed by analyzing interspike interval sequences. When periodic stimulation is u sed, the full synchronization is realized in two identical neurons, and the sync hronized response of modulated neurons can be different from the stimulation sig nal; and phase synchronization can be obtained in two neurons with different par ameters:two neurons with small parameter mismatch can be synchronized to the per iodic response different from the stimulation signal, and two neurons with big p arameter mismatch can only be synchronized to the response in phase synchronizat ion with stimulation signal. When chaotic stimulation is used, two systems can o nly be synchronized to the response being in phase synchronization with stimulat ion signal. Obviously, chaotic stimulation is more helpful in encoding and deco ding information. Analyzing the relation between the largest condition Lyapunov exponents and the stimulation strength shows that when the largest condition Lya punov exponents of the two systems are both negative is the necessary condition for synchronization. The chaotic stimulation signal can more easily synchronize two neurons than periodic stimulation signal, implying that the effect of chaoti c stimulation is stronger than periodic one, and the experiments also confirm th is conclusion.