具有时滞的帕金森模型的振荡动力学分析

研究大脑基底神经节中产生异常β振荡的起源有助于分析帕金森病的致病机理.本文系统地研究了改进的皮质-基底神经节(E-I-STN-GPe-GPi)共振模型的振荡动力学.首先,通过Routh-Hurwitz准则和稳定性理论获得了该模型局部平衡点处的稳定性与Hopf分岔发生的条件,并且推导出该共振模型存在Hopf分岔的时滞参数范围.研究发现,增加突触传输时滞能够使模型产生Hopf分岔,并且诱导β振荡的产生,使系统在健康和帕金森病这两个状态之间相互转换.其次,揭示了β振荡的产生与丘脑底核相关的突触连接强度有关.数值模拟发现,当丘脑底核同时受到兴奋性神经元集群和苍白球外侧较强的促进作用时,丘脑底核产生振荡.最后,分析了与苍白球内侧有关的参数对其产生振荡的影响,研究结果发现,当较小的苍白球外侧突触连接强度和较大的突触传输时滞共同作用时,苍白球内侧更容易发生振荡,且振幅越来越大.希望本文对E-I-STN-GPe-GPi共振模型的动力学特征的研究有助于人们理解帕金森病的致病机理和揭示帕金森病异常β振荡的来源.     

Firing synchronization of learning neuronal networks with small-world connectivity

The properties of firing synchronization of learning neuronal networks, electrically and chemically coupled ones, with small-world connectivity are studied. First, the variation properties of synaptic weights are examined. Next the effects of the synaptic learning rate on the properties of firing rate and synchronization are investigated. The influences of the coupling strength and the shortcut probability on synchronization are also explored. It is shown that synaptic learning suppresses over-excitement for the networks, helps synchronization for the electrically coupled neuronal network but destroys synchronization for the chemically coupled one. Both introducing shortcuts and increasing the coupling strength are helpful in improving synchronization of the neuronal networks. The spatio-temporal patterns illustrate and confirm the above results.     

耦合条件下大脑皮层神经振子群的能量函数

探讨了局部脑皮层网络活动中,耦合条件下的大规模神经振子群的能量消耗与神经信号编码之间的内禀关系,得到了神经元集群在阈下和阈上互相耦合时神经元膜电位变化的函数. 这个能量函数能够精确地再现神经电生理学实验中的EPSP,IPSP,动作电位以及动作电流. 最近功能性核磁共振实验证明了神经信号的编码是与能量的消耗紧密地耦合在一起的,因此研究结果表明利用能量原理研究大脑在神经网络层次上是如何进行编码的这一重大科学问题的讨论是十分有益的. 可以预计得到的能量函数将是生物学神经网络动力学稳定性计算的基础.      

Control and analysis of epilepsy waveforms in a disinhibition model of cortex network

Considering the disinhibition circuit between inhibitory neuronal populations with different time scales in cortical neural networks, here we propose a novel model to describe the occurrences and transitions of epilepsy waveforms. With the model we can successfully simulate poly-spike complexes, which are common in electrophysiological experiments and focal epilepsy patients. Meanwhile, we focus on the dynamic transitions between epilepsy waveforms and normal state and are devoted to exploring effective electrical stimulation strategies. Results show that disinhibition can induce an epileptic bidirectional transition, which is from spike and wave discharges, to poly-spike complexes and then to low-voltage rapid discharge activity, or it is reversed. And fascinating dynamical transition behaviors can be induced by varying average inhibitory synaptic gain. Interestingly, after applying two different control signals (deep brain stimulation and oscillatory input) to the system, all epilepsy waveforms can be suppressed or even eliminated. Results shed light on the pathophysiological mechanisms of epilepsy and guide clinical treatment from a theoretical viewpoint.

     

Dynamical response,information transition and energy dependence in a neuron model driven by autapse

Autapses are a class of special synapses of neurons. In those neurons, their axons are not connected to the dendrites of other neurons but are attached to their own cell bodies. The output signal of a neuron feeds back to itself, thereby allowing the neuronal firing behavior to be self-tuned. Autapses can adjust the firing accuracy of a neuron and regulate the synchronization of a neuronal system. In this paper, we investigated the information capacity and energy efficiency of a Hodgkin–Huxley neuron in the noisy signal transmission process regulated by delayed inhibitory chemical autapse for different feedback strengths and delay times. We found that the information transmission, coding efficiency, and energy efficiency are maximized when the delay time is half of the input signal period. With the increase in the inhibitory strength of autapse, this maximization is increasingly obvious. Therefore, we propose that the inhibitory autaptic structure can serve as a mechanism and enable neural information processing to be energy efficient.

     

基于信息编码的神经能量计算

通过神经元活动期间神经能量的计算, 发现关于神经元 的活动需要消耗能量的观点并不完整. 计算表明神经元在动作电位发放期间先吸收 能量然后再消耗能量. 依据这个重要发现, 能够解释当脑内神经元被激活时脑血流 量大幅增加而耗氧量却增加很少这一难以解释的神经生理学现象. 同时还能够解释外部刺激信息和知觉的产生会有同步效应这一认知神经科学界也难 以解释的现象.     

Effects of the electromagnetic radiation on cognitive performance: a model study

We constructed a two-layer network model to study the effect of electromagnetic radiation on the cognitive functions. The network model was used to simulate two cognitive tasks under the electromagnetic radiation: the visual-guided saccade task and the memory-guided saccade task. The performance of these tasks showed that the electromagnetic radiation could induce faster ramping up activities, higher level of persistent activities and shorter reaction time, but the basic functions of the network such as working memory and motor output did not impair. We found that the electromagnetic radiation have both excitatory effect and inhibitory effect on the neuronal activities of the network model, but the excitatory effect played a major role. Finally, we concluded an excitatory mechanism to explain the effects of the electromagnetic radiation on the cognitive performance.

     

Cluster synchronization and rhythm dynamics in a complex neuronal network with chemical synapses

Cluster synchronization and rhythm dynamics are studied for a complex neuronal network with the small world structure connected by chemical synapses. Cluster synchronization is considered as that in-phase burst synchronization occurs inside each group of the network but diversity may take place among different groups. It is found that both one-cluster and multi-cluster synchronization may exist for chemically excitatory coupled neuronal networks, however, only multi-cluster synchronization can be achieved for chemically inhibitory coupled neuronal networks. The rhythm dynamics of bursting neurons can be described by a quantitative characteristic, the width factor. We also study the effects of coupling schemes, the intrinsic property of neurons and the network topology on the rhythm dynamics of the small world neuronal network. It is shown that the short bursting type is robust with respect to the coupling strength and the coupling scheme. As for the network topology, more links can only change the type of long bursting neurons, and short bursting neurons are also robust to the link numbers.     

Effects of time-periodic intercoupling strength on burst synchronization of a clustered neuronal network

In this paper, we investigate the effect of time-periodic intercoupling strength on burst synchronization of a clustered neuronal network. We mainly focus on discussing the effects of amplitude and frequency of the time-periodic intercoupling strength on burst synchronization. We found that by tuning the frequency, burst synchrony of the clustered neuronal network could change from higher synchronized states to low synchronized states, and vice versa. While for the amplitude, we surprisingly found that with increasing of the amplitude, burst synchrony of the clustered neuronal network is not always enhanced. We know that synchronization has close relationship with cognitive activities and brain disorders. Thus, our results could give us some useful insight on the important role of time-dependent couplings in neuronal systems.     

关于注意和记忆的神经动力学机制

利用随机的相变动力学理论研究了一个具有不同相位的神经振子群模型,并考察神经 振子群对刺激信息的处理及神经编码的动态演化. 通过对动力学模型的数值分析,在二维相 空间上描述了神经元集群内不同振子簇发放动作电位时,数密度随时间演化的图像. 数值分 析的结果表明该模型能够用来描述注意和记忆的神经动力学机制,并且证明了只有高维的神 经动力学模型才能更深刻地描述神经元集群的动力学特性,而以往的编码模型丢失了大量有 用的神经信息.     

Fractional-order excitable neural system with bidirectional coupling

Fractional-order dynamics is applicable to biological excitable systems with strong interactions or systems with long-term memory effect. The activity of neural membrane voltage depends on the long-range correlations of ionic conductances. Such a behavior of the membrane voltage with long-range correlation can be better described with a fractional-order dynamics. A fractional-order coupled modified three-dimensional (3D) Morris–Lecar (M–L) neural system has been presented to show the variations in the firing patterns from resting state \( \rightarrow \) oscillatory pattern \( \rightarrow \) bursting and the synchronous behavior by designing a bidirectional coupling mechanism. The fractional exponents are lying between 0 and 1. The predominant controller of the changes of firing behavior is the fractional exponent. The stability of synchronization and nature of the fractional system dynamics have been analyzed. To make the investigations more convincing and biologically plausible, we consider a network of M–L oscillators with bidirectional synaptic coupling functions using global type connections and present the effectiveness of the coupling scheme.     

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities： experiments and analysis

Recent advances in the experimental and theoretical study of dynamics of neuronal electrical firing activities are reviewed. Firstly, some experimental phenomena of neuronal irregular firing patterns, especially chaotic and stochastic firing patterns, are presented, and practical nonlinear time analysis methods are introduced to distinguish deterministic and stochastic mechanism in time series. Secondly, the dynamics of electrical firing activities in a single neuron is concerned, namely, fast-slow dynamics analysis for classification and mechanism of various bursting patterns, one- or two-parameter bifurcation analysis for transitions of firing patterns, and stochastic dynamics of firing activities （stochastic and coherence resonances, integer multiple and other firing patterns induced by noise, etc.）. Thirdly, different types of synchronization of coupled neurons with electrical and chemical synapses are discussed. As noise and time delay are inevitable in nervous systems, it is found that noise and time delay may induce or enhance synchronization and change firing patterns of coupled neurons. Noise-induced resonance and spatiotemporal patterns in coupled neuronal networks are also demonstrated. Finally, some prospects are presented for future research. In consequence, the idea and methods of nonlinear dynamics are of great significance in exploration of dynamic processes and physiological functions of nervous systems.     

The collective bursting dynamics in a modular neuronal network with synaptic plasticity

In this study, how the synaptic plasticity influences the collective bursting dynamics in a modular neuronal network is numerically investigated. The synaptic plasticity is described by a modified Oja’s learning rule. The modular network is composed of some sub-networks, each of them having small-world characteristic. The result indicates that bursting synchronization can be induced by large coupling strength between different neurons, which is robust to the local dynamical parameter of individual neurons. With the emergence of synaptic plasticity, the bursting dynamics in the modular neuronal network, particularly the excitability and synchronizability of bursting neurons, is detected to be changed significantly. In detail, upon increasing synaptic learning rate, the excitability of bursting neurons is greatly enhanced; on the contrary, bursting synchronization between interacted neurons is a little suppressed by the increase in synaptic learning rate. The presented findings could be helpful to understand the important role of synaptic plasticity on neural coding in realistic neuronal network.     

A series of base functions for global analytical approach to firing table

A series of base functions has been proposed for global analytical approach to the firing table on cannons and guns. Numerical tests on the firing table of a gun of specific model prove that it is satisfactory, showing that these functions should also be useful to approach to the firing table of firearms of other models.Methods of extension and invariability analysis developed for obtaining the base functions in question should be of value as a reference to global analytical approach to a great many other numerical functions.     

A feasible neuron for estimating the magnetic field effect

Biological neurons are capable of encoding a variety of stimuli, and the synaptic plasticity can be enhanced for activating appropriate firing modes in the neural activities. Artificial neural circuits are effective to reproduce the main biophysical properties of neurons when the nonlinear circuits composed of reliable electronic components with distinct physical properties are tamed to generate similar firing patterns as biological neurons. In this paper, a simple neural circuit is proposed to estimate the effect of magnetic field on the neural activities by incorporating two physical electronic components. A magnetic flux-controlled memristor and an ideal Josephson junction in parallel connection are used to percept the induction currents induced by the magnetic field. The circuit equations are obtained according to the Kirchhoff’s theorem and an equivalent neuron model is acquired by applying scale transformation on the physical variables and parameters in the neural circuit. Standard bifurcation analysis is calculated to predict possible mode transition and evolution of firing patterns. The Hamilton energy is also obtained to find its dependence on the mode selection in electronic activities. Furthermore, External magnetic field is applied to estimate the mode transition of neural activities because the phase error and the junction current across the Josephson junction can be adjusted to change the dynamics of the neural circuit. It is found that the biophysical functional neuron can present rapid and sensitive response to external magnetic field. Nonlinear resonance is obtained when stochastic phase error is induced by external time-varying magnetic field. The neural circuit can be suitable for further calculating the collective behaviors of neurons exposed to magnetic field.

     

Thermal Convection in a Cattaneo–Fox Porous Material with Guyer–Krumhansl Effects

The Guyer–Krumhansl equation is coupled with the Cattaneo–Fox law for the temperature and heat flux fields to study thermal convection in a fluid-saturated Darcy porous material. In particular the effects of the Guyer–Krumhansl terms on oscillatory convection are studied. It is found that for a certain range of the Guyer–Krumhansl coefficient stationary convection occurs while changing the range results in oscillatory convection. Numerical results quantify this effect.     

Onset of unsteady axi-symmetric laminar natural convection in a vertical cylindrical enclosure heated at the wall

In the present study laminar transition to oscillatory convection of fluids having different Prandtl numbers in a laterally heated vertical cylindrical enclosure for different aspect ratios (melt height to crucible radius) of 2–4 is investigated numerically for 0.01 ≤ Pr ≤ 10. Numerical solution to two-dimensional axisymmetric transient Navier Stokes equations and energy equation were solved by finite volume method using SIMPLE algorithm. Numerical results illustrate that there exists a critical Rayleigh number for each Prandtl number beyond which sustained laminar oscillatory flow sets in. The oscillatory regime was characterised by the oscillation of the average kinetic energy and average thermal energy of the melt. For a given aspect ratio, critical Rayleigh number increases with Pr upto 1 and then flattens. It was observed that for low Prandtl number fluids, Pr < 1.0, critical Rayleigh number is found to increase with increase in aspect ratio while for high Prandtl number fluids, Pr ≥ 1.0, it is found to decrease with increase in aspect ratio. The influence of aspect ratio on the transient behaviour of the melt volume below and above the critical Rayleigh number was studied.     

Coherence resonance in an autaptic Hodgkin–Huxley neuron with time delay

Autapses, synapses between a neuron and itself, are believed to serve as a regulator of information processing in the nervous system. Noise, as random or unpredictable fluctuations, affects nearly all aspects of nervous function. In this work, we studied the regulatory ability of an autapse on firing behaviors of a Hodgkin–Huxley neuron in response to synaptic-like signals in the presence of noise. For weak subthreshold synaptic input, the autaptic neuron produced the similar firing behavior governed by the noise in case of either determinate or random synaptic input. The critical noise intensity necessary to trigger the spike train slightly was decreased with determinate low-frequency input. Under a strong suprathreshold synaptic current, noise-induced frequency resonance and precise responses mostly occured with a high-frequency determinate input. With a random strong synaptic input, an increase in the autaptic delay led to a resonance-like response, but had no observable effects in cases with a short delay time under a low-frequency input.     

Numerical Computations and Integrations of the Wave Resistance Green's Function

In order to develop an efficient method, using Kelvin--Havelock singularities, to compute the steady lifting flow around a ship with forward speed, the accuracy of computations of Green's function and boundary integrations have been investigated. The computations have been done using interpolation from tables for the nonoscillatory term of Green's function and using series for the oscillatory one; it has been shown that a region exists, close to the free-surface, where this last term must be computed by complete integration to ensure a prescribed error. Three schemes of boundary integrations have been studied; first boundary integrations have been performed using a Gauss method. Then, to improve accuracy, Fourier and boundary integrations have been interchanged either only for the oscillatory term or for both terms. Numerical results are compared and discussed taking into account both precision and computational time, for a submerged ellipsoid and for a lifting surface-piercing body. Received 5 February 1998 and accepted 25 September 1998