耦合Hindmarsh-Rose神经元的放电模式和完全同步

通过数值模拟和分岔分析的方法研究了Hindmarsh-Rose（HR）神经元的放电模式。当外加直流激励变化时，单个的神经元表现为静息态、周期性峰放电、周期性簇放电以及混沌的放电模式。利用快慢动力学分析的方法研究了HR神经元的动力学行为。当每个神经元表现为静息态、周期性放电和混沌时，两个耦合的神经元在一定的耦合强度下均会达到完全同步。神经元的耦合方式模拟神经元之间缝隙连接的电耦合。理论分析了完全同步的判断准则，并给出相应的数值模拟结果。电耦合HR神经元耦合系统的峰峰间期的分岔结构在耦合的作用下仍然能保持未耦合时的分岔结构。     

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     

外界电场激励下的耦合FitzHugh-Nagumo神经元系统的放电节律研究

研究了单向耦合连接的两个FitzHugh-Nagumo神经元系统的动力学行为.随外激频率的变化,系统表现出p:q锁相（一种周期振荡,q周期刺激产生p周期动作电位）,且锁相是否发生与放电状态有关.研究表明外激频率和耦合强度都可以引起系统峰峰间期（interspike Interval,ISI）分岔,而外激频率对系统放电节律的影响更为明显,研究还发现混沌态是其他放电状态的过渡态. 关键词： FHN神经元 耦合 动力学行为     

简谐噪声激励下FitzHugh-Nagumo神经元的动力学行为

研究了简谐噪声激励下的FitzHugh-Nagumo神经元模型, 其放电形式、相干共振等动力学行为均受噪声阻尼参数和频率参数的影响.选择不同的参数所得到的神经元的放电形式不同.神经元存在共振特性,对某一频率的噪声有更强的响应,在此频率参数下的峰序列更有序,出现相干共振系数的极小值.噪声的阻尼参数越大,不同的频率成分越多,神经元的响应也变得杂乱,进而导致神经元与噪声的同步变弱,峰序列相干共振系数也相应增大. 关键词： 简谐噪声 FitzHugh-Nagumo神经元 相干共振 峰峰间隔     

神经元电活动不同节律模式的几种变化过程

利用神经元Chay模型,对实验中观察到的三种放电节律模式序列进行数值模拟,并应用余维1极限环分岔分析研究了其产生机理.首先考虑的是周期性放电模式的变化过程;其次,具有不同表象的一种超临界和一种亚临界倍周期簇放电序列产生并导致混沌现象的出现,然后以不同的方式转迁到逆超临界倍周期峰放电序列;最后研究无混沌的加周期簇放电序列,得出加周期分岔仅是一种与倍周期分岔密切相关的分岔现象.     

一类新的混沌神经放电的动力学特征的实验和数学模型研究

神经元电活动理论模型Hindmarsh-Rose(HR)模型提示有位于周期1和周期2放电模式之间的一类特殊的混沌放电,但长期以来对其没有获得足够认识.依据回归映射的确定性结构和非线性预报的短期可预报性,确认了在大鼠的实验性神经起步点的实验中发现的位于周期1和周期2放电模式之间的非周期放电是混沌放电模式,还将该混沌放电模式区分为3个不同表观样式.其中1个表观形式与HR模型的仿真结果相类似,验证了HR模型的理论预期;其余2个样式与仿真结果并不相似.进一步揭示了3个表观样式的动力学特征以及相互之间的区别与联系,并与位于周期2和周期3节律之间、周期3和周期4节律之间的混沌比较了异同,也区别了从周期1到混沌再到周期2放电模式的节律转迁历程与其他的从周期1到周期2节律的分岔过程的不同.研究结果确认了该类特殊混沌节律和相应分岔过程的新特征,丰富了混沌放电节律和节律分岔序列的种类.还对仿真该混沌的多样性和非光滑特性,以及揭示该类混沌的产生途径等进行了讨论. 关键词： 混沌 神经放电模式 分岔 节律     

一类自突触作用下神经元电路的设计和模拟

神经元在自突触作用下可以诱发各类放电活动的迁移, 神经元动作电位对电自突触的响应比较敏感. 通常用包含延迟因子和增益的反馈回路电流来刻画自突触对神经元动作电位的影响. 基于Pspice软件, 设计了包含自突触效应的神经元电路, 用以延迟反馈电路来模拟电自突触对电位的调制作用. 研究结果发现: 1)在外界刺激和电自突触回路协同作用下, 神经元电路输出信号可以呈现静息态, 尖峰放电, 簇放电状态. 2)在时变增大的外界刺激下和自突触回路驱动下, 神经元电路的输出电位序列在多种电活动模式之间(静息, 尖峰放电, 簇放电)交替出现, 其机理在于自突触回路具有记忆特性, 神经元对于不同的外界刺激可以做出不同模式的响应. 3)在给定比较大外界刺激下, 改变反馈回路的增益, 发现电路输出的序列也可以呈现不同模式交替, 即神经元对于相同的刺激可以通过自我调节自突触增益来产生不同模式的响应, 其机理可能在于回路的有效反馈, 这有助于理解突触的可塑性.     

电压模式BUCK变换器输出延迟反馈混沌控制

将输出时间延迟反馈控制(TDFC)引入到电压模式BUCK变换器控制中，实现了对原系统的混沌控制.利用谐波平衡法，基于频域量化分析，确定出延迟时间和反馈增益的调节范围.同时在延迟时间比开关周期小得多的情况下，将TDFC等效为一类简单的无源反馈控制，二者仿真控制结果基本一致.最后搭建该无源反馈控制电压模式BUCK变换器实验电路，验证了所提控制方式可以快速实现系统混沌态到单周期态的过渡，而且电压和电流纹波得到减小.     

色关联噪声驱动下非线性神经元模型的相干共振

研究了关联的加性离子通道噪声和乘性突触噪声共同作用下非线性积分发放神经元模型中的相干共振现象.运用绝热近似理论和统一色噪声近似方法,得到了神经元首次点火概率分布和神经元放电峰峰间隔的变差系数的近似表达式.研究表明,首次点火概率分布和变差系数是突触噪声强度、离子通道噪声强度、乘性色噪声自相关时间和噪声关联强度的函数,适当的噪声强度、噪声自相关时间和噪声关联强度可以减小神经元发放峰峰间隔的变差系数,使系统的相干性达到最大值,从而引起神经元出现相干共振现象.同时讨论了离子通道噪声强度、突触噪声强度、乘性色噪声自相关时间和噪声关联强度对系统相干共振的影响.     

阈值耦合混沌神经元的同步研究

将阈值控制方法应用于混沌神经元团簇,构成阈值耦合混沌神经元映射,研究其时空特性.仿真实验表明,控制阈值决定了阈值耦合混沌神经元映射输出的时间周期特性,而张弛时间影响了输出的空间特性,阈值耦合混沌神经元映射输出表现出很好的聚类性.当张弛时间足够大时,阈值耦合混沌神经元映射输出实现时空完全同步.     

Models of the temporal dynamics of visual processing

Single unit recordings of neurons in primary visual cortex have demonstrated complex temporal patterns in the interspike interval return maps when presented with periodic input. Two models are tested to account for these patterns. An integrate-and-fire model is only able to replicate thein vivo data if its synaptic input is a chaotic function of time (such as a time series derived from the sinusoidally driven Duffing equation). Simpler purely periodic inputs are insufficient to replicate the experimental data. A Hodgkin-Huxley ionic model with a periodic input can replicate some of the features of the neural data, however it seems to be lacking as a complete model. These results indicate that thein vivo dynamics are not a result of the intrinsic properties of the neuron, but arise from a chaotic input to the neuron.     

Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay

The firing of a neuron model is mainly affected by the following factors:the magnetic field, external forcing current, time delay, etc. In this paper, a new time-delayed electromagnetic field coupled dual Hindmarsh-Rose neuron network model is constructed. A magnetically controlled threshold memristor is improved to represent the self-connected and the coupled magnetic fields triggered by the dynamic change of neuronal membrane potential for the adjacent neurons. Numerical simulation confirms that the coupled magnetic field can activate resting neurons to generate rich firing patterns, such as spiking firings, bursting firings, and chaotic firings, and enable neurons to generate larger firing amplitudes. The study also found that the strength of magnetic coupling in the neural network also affects the number of peaks in the discharge of bursting firing. Based on the existing medical treatment background of mental illness, the effects of time lag in the coupling process against neuron firing are studied. The results confirm that the neurons can respond well to external stimuli and coupled magnetic field with appropriate time delay, and keep periodic firing under a wide range of external forcing current.     

Spiking patterns of a hippocampus model in electric fields

We develop a model of CA3 neurons embedded in a resistive array to mimic the effects of electric fields from a new perspective. Effects of DC and sinusoidal electric fields on firing patterns in CA3 neurons are investigated in this study. The firing patterns can be switched from no firing pattern to burst or from burst to fast periodic firing pattern with the increase of DC electric field intensity. It is also found that the firing activities are sensitive to the frequency and amplitude of the sinusoidal electric field. Different phase-locking states and chaotic firing regions are observed in the parameter space of frequency and amplitude. These findings are qualitatively in accordance with the results of relevant experimental and numerical studies. It is implied that the external or endogenous electric field can modulate the neural code in the brain. Furthermore, it is helpful to develop control strategies based on electric fields to control neural diseases such as epilepsy.     

Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse

Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is proposed in this paper. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional-order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of Hindmarsh-Rose (HR) neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional-order on the firing behavior are discussed by time series, phase diagram, Lyapunov exponent and inter spike interval (ISI) bifurcation diagram. Three coexisting firing patterns, including irregular asymptotically periodic (A-periodic) bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values, are observed. It is also revealed that the fractional-order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional-order is designed to verify the numerical simulations.     

Control of firing activities in thermosensitive neuron by activating excitatory autapse

Temperature has distinct influence on the activation of ion channels and the excitability of neurons, and careful change in temperature can induce possible mode transition in the neural activities. The formation and development of autapse connection to neuron can enhance its self-adaption to external stimulus, and thus the firing patterns in neuron can be controlled effectively. The autapse is activated to drive a thermosensitive neuron, which is developed from the FitzHugh–Nagumo neural circuit by incorporating a thermistor, and the dynamics in the neural activities is explored to find mode dependence on the temperature and autaptic current. It is found that the firing modes can be controlled by temperature, and the neuron is wakened from resting state to periodic oscillation with the increase of temperature. Furthermore, the intensity and the intrinsic time delay in the autapse are respectively adjusted to control the neural activities, and it is confirmed that appropriate setting for autaptic current can balance and enhance the temperature effect on the neural activities.     

Adaptive modification of the delayed feedback control algorithm with a continuously varying time delay

We propose a simple adaptive delayed feedback control algorithm for stabilization of unstable periodic orbits with unknown periods. The state dependent time delay is varied continuously towards the period of controlled orbit according to a gradient-descent method realized through three simple ordinary differential equations. We demonstrate the efficiency of the algorithm with the Rössler and Mackey-Glass chaotic systems. The stability of the controlled orbits is proven by computation of the Lyapunov exponents of linearized equations.     

Coullet混沌系统的演化和控制实验

构建了Coullet混沌系统的硬件实验电路,改变系统的参数,可以从示波器上观察系统从稳定周期状态演变到混沌状态的分岔过程.采用非线性反馈控制方法实现了对Coullet混沌系统的有效控制,改变反馈控制增益,可以将Coullet系统从混沌状态控制到稳定的周期状态.     

Partial state feedback control of chaotic neural network and its application

The chaos control in the chaotic neural network is studied using the partial state feedback with a control signal from a few control neurons. The controlled CNN converges to one of the stored patterns with a period which depends on the initial conditions, i.e., the set of control neurons and other control parameters. We show that the controlled CNN can distinguish between two initial patterns even if they have a small difference. This implies that such a controlled CNN can be feasibly applied to information processing such as pattern recognition.     

Synchronization of chaos in resistive-capacitive-inductive shunted Josephson junctions

We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions （RCLSJJs） by using another chaotic RCLSJJ as a driving system. Numerical simulations show that whether the two RCLSJJs are chaotic or not before being driven, they can realize chaotic synchronization with a suitable driving intensity, under which the maximum condition Lyapunov exponent （MCLE） is negative. On the other hand, if the driving system is in different periodic states or chaotic states, the two driven RCLSJJs can be controlled into the periodic states with different period numbers or chaotic states but still maintain the synchronization.     

Dynamical response of a neuron–astrocyte coupling system under electromagnetic induction and external stimulation

Previous studies have observed that electromagnetic induction can seriously affect the electrophysiological activity of the nervous system. Considering the role of astrocytes in regulating neural firing, we studied a simple neuron–astrocyte coupled system under electromagnetic induction in response to different types of external stimulation. Both the duration and intensity of the external stimulus can induce different modes of electrical activity in this system, and thus the neuronal firing patterns can be subtly controlled. When the external stimulation ceases, the neuron will continue to fire for a long time and then reset to its resting state. In this study, "delay" is defined as the delayed time from the firing state to the resting state, and it is highly sensitive to changes in the duration or intensity of the external stimulus. Meanwhile, the self-similarity embodied in the aforementioned sensitivity can be quantified by fractal dimension. Moreover, a hysteresis loop of calcium activity in the astrocyte is observed in the specific interval of the external stimulus when the stimulus duration is extended to infinity, since astrocytic calcium or neuron electrical activity in the resting state or during periodic oscillation depends on the initial state. Finally, the regulating effect of electromagnetic induction in this system is considered. It is clarified that the occurrence of "delay" depends purely on the existence of electromagnetic induction. This model can reveal the dynamic characteristics of the neuron–astrocyte coupling system with magnetic induction under external stimulation. These results can provide some insights into the effects of electromagnetic induction and stimulation on neuronal activity.