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     

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.     

一种基于非完整二维相空间分量置换的混沌检测方法

由于混沌时间序列和随机过程具有很多类似的性质, 因而在实际中很难将两者区分开来. 混沌信号检测与识别是混沌时间序列分析中一个重要的课题. 混沌信号是由确定性的混沌映射或混沌系统产生的, 相比于高斯白噪声序列, 其在非完整的二维相空间中表现出更加丰富的结构特性. 本文通过研究混沌时间序列和高斯白噪声序列在非完整二维相空间中的分布特性, 利用混沌信号的非线性动力学特性, 提出了一种基于非完整二维相空间分量置换的混沌信号检测方法. 该方法首先由接收序列得到非完整的二维相空间, 基于第一维分量大小关系实现对第二维分量的置换与分组, 进一步求得F检验统计量. 然后利用混沌系统的局部特性, 获取非完整二维相空间的动力学结构信息, 实现对混沌序列的有效检测. 在高斯白噪声条件下对多种混沌信号进行了信号检测的数值仿真. 仿真结果表明: 相比置换熵检测, 本文所提算法所需数据量小、计算简单以及具有更低的时间复杂度, 同时对噪声具有更好的鲁棒性.     

涨落作用下周期驱动的分数阶过阻尼棘轮模型的混沌输运现象

考虑涨落作用下周期驱动的过阻尼分数阶棘轮模型, 通过模型的数值求解, 研究确定性棘轮的混沌特性与噪声的作用对输运行为的影响, 进而讨论过阻尼分数阶分子马达反向输运的机理. 分析表明: 随着势垒高度、 势不对称性与模型记忆性的变化, 随机棘轮的反向输运并不必然地要求确定性棘轮也反向输运; 随着模型阶数的减小, 亦即分数阻尼介质记忆性的增强, 确定性棘轮在反向输运之前会经历一个周期倍化导致的混沌状态, 但在噪声作用下, 反向流的发生会提前, 即混沌状态的确定性棘轮在噪声的作用下即可进行反向输运. 也就是说, 噪声能定性地改变棘轮的输运状态: 从无噪声时的混沌运动到有噪声时的定向输运. 这是过阻尼随机棘轮反向输运的一种机理, 也是噪声在定向输运过程中发挥积极作用的一个体现.     

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     

一种新的时间序列确定性辨识方法

提出一种新的基于辛几何谱的时间序列确定性检测方法，通过计算原始时间序列及其替代数据的辛几何谱，利用非参数Mann-Whitney 秩和检验方法，可有效地辨别确定性混沌过程和随机过程.通过对常见的随机过程，Lorenz，Rssler，Mackey-Glass，高维耦合方程的仿真检验，说明了方法的有效性. 并通过用Santa Fe测试集中两个序列检验了其对实际时间序列的适用性，最后研究不同数据长度和不同强度噪声对该方法性能的影响说明了其鲁棒性.     

Pre-B?tzinger复合体的从簇到峰放电的同步转迁及分岔机制

Pre-Bötzinger复合体是兴奋性耦合的神经元网络,通过产生复杂的放电节律和节律模式的同步转迁参与调控呼吸节律.本文选用复杂簇和峰放电节律的单神经元数学模型构建复合体模型,仿真了与生物学实验相关的多类同步节律模式及其复杂转迁历程,并利用快慢变量分离揭示了相应的分岔机制.当初值相同时,随着兴奋性耦合强度的增加,复合体模型依次表现出完全同步的“fold/homoclinic”,“subHopf/subHopf”簇放电和周期1峰放电.当初值不同时,随耦合强度增加,表现为由“fold/homoclinic”,到“fold/fold limit cycle”、到“subHopf/subHopf”与“fold/fold limit cycle”的混合簇放电、再到“subHopf/subHopf”簇放电的相位同步转迁,最后到反相同步周期1峰放电.完全(同相)同步和反相同步的周期1节律表现出了不同分岔机制.反相峰同步行为给出了与强兴奋性耦合容易诱发同相同步这一传统观念不同的新示例.研究结果给出了preBötzinger复合体的从簇到峰放电节律的同步转迁规律及复杂分岔机制,反常同步行为丰富了非线性动力学的内涵.     

随机Bonhoeffer-Van der Pol系统的随机混沌控制

讨论了具有有界随机参数的随机Bonhoeffer-Van der Pol系统的随机混沌现象，并利用噪声对其进行控制.首先运用Chebyshev多项式逼近的方法，将随机Bonhoeffer-Van der Pol系统转化为等价的确定性系统，使原系统的随机混沌控制问题转换为等价的确定性系统的确定性混沌控制问题，继而可用Lyapunov指数指标来研究等价确定性系统的确定性混沌现象和控制问题.数值结果表明，随机Bonhoeffer-Van der Pol系统的随机混沌现象与相应的确定性Bonhoeffer-Van der Pol系统极为相似.利用噪声控制法可将混沌控制到周期轨道，但是在随机参数及其强度的影响下也呈现出一些特点.     

Josephson结的动力学行为(Ⅰ)

本文对射频电流驱动下的包含干涉项电流的Josephson结方程进行了大量的数值研究工作。我们发现,对应于不同的参数范围,分别出现混沌行为、倍周期分岔序列、混沌带的反序列以及阵发混沌现象。我们也计算了2ⁿP序列的收敛因子δ_n和功率谱中2^k与2^k+1分频的平均峰高之比Φ(k)/Φ(k+1)。另外,还研究了周期解的对称性以及它与通向混沌途径的关系。 关键词：     

混沌系统的遗传神经网络控制

提出遗传神经网络控制混沌新方法.将小扰动技术和周期控制技术结合起来，用遗传算法训练神经网络，使之成为混沌控制器.对Henon映射和Logistic映射的仿真结果说明控制器能产生小扰动控制序列信号，将混沌振荡转变成规则运动状态.该方法无需了解动态系统数学模型，具有一定抗噪声干扰能力，可将它推广应用到其他混沌系统的控制中. 关键词： 遗传算法 神经网络 混沌 周期控制     

Two Different Bifurcation Scenarios in Neural Firing Rhythms Discovered in Biological Experiments by Adjusting Two Parameters

Two different bifurcation scenarios, one is novel and the other is relatively simpler, in the transition procedures of neural firing patterns are studied in biological experiments on a neural pacemaker by adjusting two parameters. The experimental observations are simulated with a relevant theoretical model neuron. The deterministic non-periodic firing pattern lying within the novel bifurcation scenario is suggested to be a new case of chaos, which has not been observed in previous neurodynamical experiments.     

Bursting and spiking due to additional direct and stochastic currents in neuron models

Neurons at rest can exhibit diverse firing activities patterns in response to various external deterministic and random stimuli, especially additional currents. In this paper, neuronal firing patterns from bursting to spiking, induced by additional direct and stochastic currents, are explored in rest states corresponding to two values of the parameter $V_{\rm K}$ in the Chay neuron system. Three cases are considered by numerical simulation and fast/slow dynamic analysis, in which only the direct current or the stochastic current exists, or the direct and stochastic currents coexist. Meanwhile, several important bursting patterns in neuronal experiments, such as the period-1 ``circle/homoclinic" bursting and the integer multiple ``fold/homoclinic" bursting with one spike per burst, as well as the transition from integer multiple bursting to period-1 ``circle/homoclinic" bursting and that from stochastic ``Hopf/homoclinic" bursting to ``Hopf/homoclinic" bursting, are investigated in detail.     

Delayed excitatory self-feedback-induced negative responses of complex neuronal bursting patterns

In traditional viewpoint, excitatory modulation always promotes neural firing activities. On contrary, the negative responses of complex bursting behaviors to excitatory self-feedback mediated by autapse with time delay are acquired in the present paper. Two representative bursting patterns which are identified respectively to be "Fold/Big Homoclinic"bursting and "Circle/Fold cycle" bursting with bifurcations are studied. For both burstings, excitatory modulation can induce less spikes per burst for suitable time delay and strength of the self-feedback/autapse, because the modulation can change the initial or termination phases of the burst. For the former bursting composed of quiescent state and burst, the mean firing frequency exhibits increase, due to that the quiescent state becomes much shorter than the burst. However, for the latter bursting pattern with more complex behavior which is depolarization block lying between burst and quiescent state, the firing frequency manifests decrease in a wide range of time delay and strength, because the duration of both depolarization block and quiescent state becomes long. Therefore, the decrease degree of spike number per burst is larger than that of the bursting period, which is the cause for the decrease of firing frequency. Such reduced bursting activity is explained with the relations between the bifurcation points of the fast subsystem and the bursting trajectory. The present paper provides novel examples of paradoxical phenomenon that the excitatory effect induces negative responses, which presents possible novel modulation measures and potential functions of excitatory self-feedback/autapse to reduce bursting activities.     

兴奋性自突触引起神经簇放电频率降低或增加的非线性机制

兴奋和抑制性作用分别会增强和压制神经电活动,这是神经调控的通常观念,在神经信息处理中起重要作用.本文选取了放电簇和阈下振荡相交替、放电簇谷值小于阈下振荡谷值的Homoclinic/Homoclinic型簇放电,研究发现时滞和强度合适的兴奋性自突触电流作用在放电簇的谷值附近时,能引起簇内放电个数降低,并进而导致平均放电频率降低,这是不同于通常观念的新现象.进一步,用快慢变量分离获得的分岔和相轨迹,揭示了阈下振荡和放电簇分别对应快子系统的阈下和阈上极限环,兴奋性自突触电流引起阈上极限环向阈下极限环的转迁导致放电提前结束是频率降低原因.并与近期在Fold/Homoclinic簇放电报道的兴奋性自突触诱发的簇内放电个数降低但放电频率增加的现象和机制进行了比较.研究结果丰富了神经电活动的反常现象并揭示了背后的非线性机制,给出了调控簇放电的新手段,揭示了兴奋性自突触的潜在功能.     

Response of Hodgkin–Huxley stochastic bursting neuron to single-pulse stimulus

We investigate Hodgkin–Huxley neuron model with external Gaussian noise in the range of parameters where it exhibits bistability of silent and firing states, and noise-induced bursts occur. We study the response of the system to brief single pulse of current. When noise amplitude increases, the delay time between the stimulus and the first spike decreases substantially even for subthreshold stimulus. The mean number of spikes in a post-stimulus burst has a maximum in a certain range of noise amplitudes. Therefore, we found that Hodgkin–Huxley neuron in the stochastic bursting regime has more improved sensitivity to single-pulse stimulus than in the silent one.     

Transition from deterministic to stochastic deformation

Theory predicts that deformation that occurs by emission of strain bursts falls into two regimes, one in which the burst emission remains a stochastic process as strain increases, and another in which the emission of bursts settles into a deterministic process for large strains. The stochastic regime occurs when the burst emission rate decreases with strain, and in this case, large statistical scatter persists in the stress–strain response on repeated measurements. The deterministic regime occurs when the emission rate increases with strain, and the scatter in the corresponding stress–stress behaviour diminishes at large strains. The strength at the same strain in the stochastic regime is also higher than in the deterministic regime. Factors that affect the burst emission rate include the number of sources as well as the stress dependence of the efficiency of the sources.     

Dynamical phases of the Hindmarsh-Rose neuronal model: studies of the transition from bursting to spiking chaos

The dynamical phases of the Hindmarsh-Rose neuronal model are analyzed in detail by varying the external current I. For increasing current values, the model exhibits a peculiar cascade of nonchaotic and chaotic period-adding bifurcations leading the system from the silent regime to a chaotic state dominated by bursting events. At higher I-values, this phase is substituted by a regime of continuous chaotic spiking and finally via an inverse period doubling cascade the system returns to silence. The analysis is focused on the transition between the two chaotic phases displayed by the model: one dominated by spiking dynamics and the other by bursts. At the transition an abrupt shrinking of the attractor size associated with a sharp peak in the maximal Lyapunov exponent is observable. However, the transition appears to be continuous and smoothed out over a finite current interval, where bursts and spikes coexist. The beginning of the transition (from the bursting side) is signaled from a structural modification in the interspike interval return map. This change in the map shape is associated with the disappearance of the family of solutions responsible for the onset of the bursting chaos. The successive passage from bursting to spiking chaos is associated with a progressive pruning of unstable long-lasting bursts.     

Bursting as a source for predictability in biological neural network activity

The role of bursting as a unit of neural information has received considerable support in the recent years. Experimental evidence shows that in many different neural systems, e.g. visual cortex or hippocampus, bursting is essential for coding and processing. We have recently demonstrated (Menendez de la Prida et al., 1996) the spontaneous presence of bursts in in vitro hippocampal slices from newborn animals, providing a good system to investigate bursting dynamics in physiological conditions. Here we analyze the interspike intervals (ISIs) of five intracellularly recorded cells from immature hippocampal networks. First, we test the time series against Poisson processes, typical of pure random behavior, using the Kolmogorov-Smirnov test. Only 2/5 records strongly deviate from Poisson process. Nonlinear diction tests are then applied to compare original series with its Gaussian-scaled random phase surrogates and signs of short time predictability are observed (1/5). This predictability is originated by the intrinsic structure of bursts, in an otherwise purely random process, and can be removed completely by eliminating the bursts from the original time series. Here we introduce this method of eliminating bursts to get insight into the nonlinear dynamics of firing. Also the interburst intervals are indistinguishable from pure noise. The analysis of unstable periodicities within the bursts in the original ISIs shows that signs of nonlinearities can be statistically differentiated from their surrogate realizations (Pierson-Moss method). We discuss the computational implication of these results.     

三个不同时间尺度的电耦合模型的组合簇放电

胰岛中间隙连接的胰腺β细胞的簇放电行为对胰岛素分泌起着重要的作用. 本文利用了最小的phantom 簇放电模型, 研究两个电耦合胰腺β细胞具有簇同步的组合簇放电, 其膜电位表现出一个长簇和几个短簇组成的放电簇集和振幅先减小后增大的小振幅阈下振荡的相互转迁. 在两个慢变量和快的膜电位的三维空间中, 分别考虑了中慢变量和慢慢变量作为分岔参数的多层次的快慢动力学分析, 研究这两个时间尺度不同的慢变量如何共同或单独地控制着这种组合簇放电的复杂动力学行为. 特别地, 探讨了耦合强度引起的组合簇放电的每个簇集中短簇个数变化的内在机理. 关键词： 电耦合 具有不同时间尺度的慢变量 组合簇放电 快慢动力学分析