延迟自反馈控制Hindmarsh-Rose神经元的混沌运动

Chaotic control of Hindmarsh-Rose neuron by delayed self-feedback

利用线性时间延迟自反馈方法,研究单个Hindmarsh-Rose(H-R)神经元模型混沌动力学模式的控制问题.分别将增益因子和时间延迟作为控制参数,通过数值模拟分析,发现在增益因子和时间延迟两个参数组合的一些范围内,混沌动力学模式的H-R神经元运动可自动被控制成时间间隔意义上的单峰、2峰、3峰及4峰的周期或多倍周期模式.延迟时间的选取并无特别要求,不必和嵌入在混沌吸引子内的某不稳周期轨道的周期相同,延迟控制自适应地引导混沌轨到相应的放电峰峰间隔的周期模式上.

The control problems of chaotic dynamical patterns of single Hindmarsh-Rose neuron model are studied by using delayed feedback self-control method. Taking gain factor and time delay as controlling parameters respectively, in some ranges of the combination of gain factor and time-delay, we find that the chaotic burst pattern of inter-spike interval sequences of H-R neuron can be controlled to a single-spike period, double-spikes period, 3-or 4-spikes period pattern or multi-period of these patterns for inter-spike interval as the results of numerical simulation analysis. Choice of delay is in-dependent and doesn＇t rely on the period of unstable periodic orbits embedded within chaotic attractor. The chaotic burst orbit will be controlled to a certain type of periodic patterns of inter-spike interval automatically.