混沌神经元的非线性延迟反馈自适应控制

Adaptive Control of Chaotic Neuron by Nonlinear Time Delay Feedback

利用非线性时间延迟自反馈控制方法,研究单个Hindmarsh-Rose(H-R)神经元模型从混沌动力学模式转变为周期模式的自适应控制问题。在单个H-R神经元模型运动微分方程中的第一个微分方程的右端加上一个三次方的非线性延迟自反馈项,并分别将增益因子和时间延迟作为控制参数,给出混沌神经元动力学模式被控制的分岔图。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,混沌放电模式的H-R神经元可被自动控制到某一周期模式。被控制的周期模式大都集中在1,2,3,4,6峰周期或多倍周期模式。延迟时间的选取无特别要求,并不像其他混沌系统所要求的必须和嵌入在混沌吸引子内的某不稳周期轨道的周期相同,延迟控制可自适应地引导混沌放电模式到相应的放电峰峰间隔意义上的周期模式,实现信息识别的目的。

In this paper, a nonlinear method is used for the chaotic control of a single H-R neuronal model. The nonlinear time delay feedback function is added to the right hand side of the first differential equation of equations of a single Hindmarsh-Rose （H-R） neuron model. Gain factor and time-delay are taken as control parameters. Through the numerical calculations and analyses, a certain range of the combination of gain factor and time-delay is found, in which, the chaotic burst pattern of inter-spike interval sequences of H-R neuron can be controlled onto a spikes-period pattern or a multi-period of these patterns automatically. The main periodic patterns of H-R neuron are patterns of the spike-period, double spikes-period, 3 spikes-period, 4 spikes-period and 6 spikes-period and their multi-period pattern. The bifurcation diagrams of the chaotic neuron under control are provided. Choice of delay does not depend and rely on the period of unstable periodic orbits embedded within the chaotic attractor. The chaotic burst orbit will be controlled onto the certain type of periodic patterns of inter-spike interval automatically, to achieve the purposes of information identification.