Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a biophysical model of neuronal dynamics

In this paper, complex dynamical synchronization in a non-linear model of a neural system is studied, and the computational significance of the behaviours is explored. The local neural dynamics is determined by voltage- and ligand-gated ion channels and feedback between densely interconnected excitatory and inhibitory neurons. A mesoscopic array of local networks is modelled by introducing coupling between the local networks via weak excitatory-to-excitatory connectivity. It is shown that with modulation of this long-range synaptic coupling, the system undergoes a transition from independent oscillations to stable chaotic synchronization. Between these states exists a 'weakly' stable state associated with complex, intermittent behaviour in the temporal domain and clusters of synchronous regions in the spatial domain. The paper concludes with a discussion of the putative relevance of such processes in the brain, including the role of neuromodulatory systems and the mechanisms underlying sensory perception, adaptation, computation and complexity.     

How noise affects the synchronization properties of recurrent networks of inhibitory neurons

GABAergic interneurons play a major role in the emergence of various types of synchronous oscillatory patterns of activity in the central nervous system. Motivated by these experimental facts, modeling studies have investigated mechanisms for the emergence of coherent activity in networks of inhibitory neurons. However, most of these studies have focused either when the noise in the network is absent or weak or in the opposite situation when it is strong. Hence, a full picture of how noise affects the dynamics of such systems is still lacking. The aim of this letter is to provide a more comprehensive understanding of the mechanisms by which the asynchronous states in large, fully connected networks of inhibitory neurons are destabilized as a function of the noise level. Three types of single neuron models are considered: the leaky integrate-and-fire (LIF) model, the exponential integrate-and-fire (EIF), model and conductance-based models involving sodium and potassium Hodgkin-Huxley (HH) currents. We show that in all models, the instabilities of the asynchronous state can be classified in two classes. The first one consists of clustering instabilities, which exist in a restricted range of noise. These instabilities lead to synchronous patterns in which the population of neurons is broken into clusters of synchronously firing neurons. The irregularity of the firing patterns of the neurons is weak. The second class of instabilities, termed oscillatory firing rate instabilities, exists at any value of noise. They lead to cluster state at low noise. As the noise is increased, the instability occurs at larger coupling, and the pattern of firing that emerges becomes more irregular. In the regime of high noise and strong coupling, these instabilities lead to stochastic oscillations in which neurons fire in an approximately Poisson way with a common instantaneous probability of firing that oscillates in time.     

Input Shaping of the Synchronous Generator for Reduction of Self‐induced Oscillations

This article suggests the application of input shaping for the elimination of electromechanical oscillations arising from changes in the operating point of the synchronous generator. Poorly damped poles are the cause of electromechanical oscillations of the synchronous generator. Various power system stabilizers (PSS) are now used to reduce the electromechanical oscillations. Input shaping is a feedforward control and therefore does not require the measurement of electrical and mechanical quantities of the synchronous generator unlike the PSS. It is possible to apply the input shaping for the excitation system of synchronous generators with or without PSS.     

Correlated firing improves stimulus discrimination in a retinal model

Synchronous firing limits the amount of information that can be extracted by averaging the firing rates of similarly tuned neurons. Here, we show that the loss of such rate-coded information due to synchronous oscillations between retinal ganglion cells can be overcome by exploiting the information encoded by the correlations themselves. Two very different models, one based on axon-mediated inhibitory feedback and the other on oscillatory common input, were used to generate artificial spike trains whose synchronous oscillations were similar to those measured experimentally. Pooled spike trains were summed into a threshold detector whose output was classified using Bayesian discrimination. For a threshold detector with short summation times, realistic oscillatory input yielded superior discrimination of stimulus intensity compared to rate-matched Poisson controls. Even for summation times too long to resolve synchronous inputs, gamma band oscillations still contributed to improved discrimination by reducing the total spike count variability, or Fano factor. In separate experiments in which neurons were synchronized in a stimulus-dependent manner without attendant oscillations, the Fano factor increased markedly with stimulus intensity, implying that stimulus-dependent oscillations can offset the increased variability due to synchrony alone.     

Fast global oscillations in networks of integrate-and-fire neurons with low firing rates.

We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons --> infinity, the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized. The activity becomes oscillatory when the inhibitory feedback is strong enough. The period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input. In large but finite networks, the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold. Their characteristics are determined as functions of systems parameters in these two different regions. The results are found to be in good agreement with numerical simulations.     

High-frequency, depressing inhibition facilitates synchronization in globally inhibitory networks

Motivated by the study of sharp wave-associated ripples, high-frequency (approximately 200 Hz) extracellular field oscillations observed in the CA1 region of the rat hippocampus during slow-wave sleep and periods of behavioural immobility, we consider a single inhibitory neuron synapsing onto a network of uncoupled, excitatory neurons. The inhibitory synapse is depressing and has a small synaptic delay. Each excitatory cell provides instantaneous, positive feedback to the inhibitory cell. We show that the interneuron can rapidly synchronize the action potentials of the pyramidal cells if the frequency of inhibitory input is increased in a ramp-like manner as occurs during the ripple. We show that the basin of attraction of the synchronous solution is larger when the inhibition frequency is gradually increased as opposed to remaining constant.     

基于虚拟柴油发电机控制策略的岸电电源设计

岸电电源需要与各种类型的船舶电源系统进行无缝切换,而传统的基于虚拟同步发电机控制策略的岸电电源只能模拟同步发电机的机械特性,与船舶的主电源——柴油发电机还略有差异。因此并网运行常出现大的超调和低频振荡等问题。针对这些问题,首先对柴油发电机(DG)和传统的虚拟同步发电机控制进行建模分析,然后针对DG动态响应速度慢、电压频率易波动的问题,提出了虚拟柴油发电机控制策略。该控制策略利用补偿网络的惯性抑制了频率的波动,微分环节提高系统的动态特性。最后,建立一套100kVA岸电电源系统样机系统,试验结果验证了该控制方法的有效性。     

基于虚拟柴油发电机控制策略的岸电电源设计

岸电电源需要与各种类型的船舶电源系统进行无缝切换,而传统的基于虚拟同步发电机控制策略的岸电电源只能模拟同步发电机的机械特性,与船舶的主电源——柴油发电机还略有差异。因此并网运行常出现大的超调和低频振荡等问题。针对这些问题,首先对柴油发电机(DG)和传统的虚拟同步发电机控制进行建模分析,然后针对DG动态响应速度慢、电压频率易波动的问题,提出了虚拟柴油发电机控制策略。该控制策略利用补偿网络的惯性抑制了频率的波动,微分环节提高系统的动态特性。最后,建立一套100kVA岸电电源系统样机系统,试验结果验证了该控制方法的有效性。     

Pattern recognition through compatibility of excitatory and inhibitory rhythms

A pattern recognition mechanism (“windowing mechanism”) is proposed that is based on Hebbian memory and oscillatory inhibition. It is related to properties of cortical gamma oscillations as expressed with the communication-through-coherence hypothesis. The rhythm dominating among excitatory units is imprinted on the inhibitory units through columnar couplings. Excitatory units that participate in the dominating rhythm may escape the feedback from the inhibitory pool through being active in the time windows given by the minima of the inhibitory effect. The activity of other units is suppressed. Constituting an excitatory rhythm that is compatible with the inhibitory one, the participating units comprise the winning patterns. This windowing mechanism is specified through giving an oscillatory network model and demonstrating it with image processing examples. Thereby, we also provide a gradient system formulation for inhibitory generation of synchrony.     

Asynchronous states and the emergence of synchrony in large networks of interacting excitatory and inhibitory neurons

We investigate theoretically the conditions for the emergence of synchronous activity in large networks, consisting of two populations of extensively connected neurons, one excitatory and one inhibitory. The neurons are modeled with quadratic integrate-and-fire dynamics, which provide a very good approximation for the subthreshold behavior of a large class of neurons. In addition to their synaptic recurrent inputs, the neurons receive a tonic external input that varies from neuron to neuron. Because of its relative simplicity, this model can be studied analytically. We investigate the stability of the asynchronous state (AS) of the network with given average firing rates of the two populations. First, we show that the AS can remain stable even if the synaptic couplings are strong. Then we investigate the conditions under which this state can be destabilized. We show that this can happen in four generic ways. The first is a saddle-node bifurcation, which leads to another state with different average firing rates. This bifurcation, which occurs for strong enough recurrent excitation, does not correspond to the emergence of synchrony. In contrast, in the three other instability mechanisms, Hopf bifurcations, which correspond to the emergence of oscillatory synchronous activity, occur. We show that these mechanisms can be differentiated by the firing patterns they generate and their dependence on the mutual interactions of the inhibitory neurons and cross talk between the two populations. We also show that besides these codimension 1 bifurcations, the system can display several codimension 2 bifurcations: Takens-Bogdanov, Gavrielov-Guckenheimer, and double Hopf bifurcations.     

Spike-timing-dependent plasticity in small-world networks

Biologically plausible excitatory neural networks develop a persistent synchronized pattern of activity depending on spontaneous activity and synaptic refractoriness (short term depression). By fixed synaptic weights synchronous bursts of oscillatory activity are stable and involve the whole network. In our modeling study we investigate the effect of a dynamic Hebbian-like learning mechanism, spike-timing-dependent plasticity (STDP), on the changes of synaptic weights depending on synchronous activity and network connection strategies (small-world topology). We show that STDP modifies the weights of synaptic connections in such a way that synchronization of neuronal activity is considerably weakened. Networks with a higher proportion of long connections can sustain a higher level of synchronization in spite of STDP influence. The resulting distribution of the synaptic weights in single neurons depends both on the global statistics of firing dynamics and on the number of incoming and outgoing connections.     

Smooth transition between different gaits of a hexapod robot via a central pattern generators algorithm

This paper focuses on the topic of smooth gait transition of a hexapod robot by a proposed central pattern generator (CPG) algorithm. Through analyzing the movement characteristics of the real insects, it is easy to generate kinds of gait patterns and achieve their smooth transition if we employ a series of oscillations with adjustable phase lag. Based on this concept, a CPG model is proposed, which is constructed by an isochronous oscillators and several first-order low-pass filters. As an application, a hexapod robot and its locomotion control are introduced by converting the CPG signal to robot’s joint space. Simulation and real world experiment are completed to demonstrate the validity of the proposed CPG model. Through measuring the position of the body center and the distance between footpoints and ground, the smooth gait transition can be achieved so that the effectiveness of the proposed method is verified.     

Statistical signs of common inhibitory feedback with delay

Cross-correlation histograms (CCHs) sometimes exhibit an isolated central peak flanked by two troughs. What can cause this pattern? The absence of CCH satellite peak makes an oscillatory common input doubtful. It is here shown using a simple counting model that a common inhibitory feedback with delay can account for this pattern.     

Dynamics of strongly-coupled spiking neurons

We present a dynamical theory of integrate-and-fire neurons with strong synaptic coupling. We show how phase-locked states that are stable in the weak coupling regime can destabilize as the coupling is increased, leading to states characterized by spatiotemporal variations in the interspike intervals (ISIs). The dynamics is compared with that of a corresponding network of analog neurons in which the outputs of the neurons are taken to be mean firing rates. A fundamental result is that for slow interactions, there is good agreement between the two models (on an appropriately defined timescale). Various examples of desynchronization in the strong coupling regime are presented. First, a globally coupled network of identical neurons with strong inhibitory coupling is shown to exhibit oscillator death in which some of the neurons suppress the activity of others. However, the stability of the synchronous state persists for very large networks and fast synapses. Second, an asymmetric network with a mixture of excitation and inhibition is shown to exhibit periodic bursting patterns. Finally, a one-dimensional network of neurons with long-range interactions is shown to desynchronize to a state with a spatially periodic pattern of mean firing rates across the network. This is modulated by deterministic fluctuations of the instantaneous firing rate whose size is an increasing function of the speed of synaptic response.     

A central pattern generator circuit for rhythmic robotic chewing locomotion in low-voltage analog CMOS technology

It is well known that rhythmic animal locomotive behavior such as walking, running, swimming, and flying is driven by biological neural networks with a phase-locked oscillatory behavior called a central pattern generator (CPG). This article describes a CPG circuit for the locomotion control of rhythmic robotic chewing. A two-neuron CPG model, which is slightly modified from the Matsuoka oscillator model, was implemented in a low-voltage analog CMOS circuit using the IBM 130 nm CMOS technology. A new concept of a −3 dB rhythmic chewing bandwidth has been introduced to account for the time constants in the model. The significance of the −3 dB chewing bandwidth is that any effort by the animal to chew at a faster rate than the inherent chewing bandwidth of that animal is likely to result in a reduced chewing force. Compared with the digital implementation, the analog CPG consumes less power and occupies less silicon area. The analog CPG consists of compensated current-mode low-pass filters and current mirrors implementing the neurons, which are cross-connected by inhibitory synaptic links. There are two tonic sensory inputs, two internal states, and two adaptation outputs for muscles for the CPG circuit.     

电力系统耦合双回路数学建模及仿真

对短距离电力系统数字仿真时，可按物理设备对系统分块，将电力传输线、同步发电机、变压器、综合负载分别作为独立模块建模，各模块连接处用解耦电压源替代，这样各模块可平行地进行数字积分。本文用集总参数建立了双回线而且考虑两回线之间以及每回线各相之间都分别存在着耦合的双回传输线模块数字实时仿真模型，并在已知同步发电机与综合负载模型的基础上，给出了相应的数值积分方法。     

基于先进复合控制算法的同步发电机励磁分布式微机控制系统设计

设计一种新型同步发电机励磁系统,除了采用串联型PID控制算法外,还辅助以PSS、LOEC、NOEC控制算法分别用于改善电力系统小干扰稳定性、抑制各种频率的低频振荡和系统暂态稳定、静态稳定并抑制电力系统功率振荡。给出了系统硬件框图、算法和主程序流程图,并对系统运行过程进行了阐述。     

磁悬浮飞轮储能系统机电耦合非线性动力学研究

针对磁悬浮飞轮储能系统的"磁悬浮飞轮-发电机"机电耦合非线性动力学特性进行研究.通过推导磁悬浮飞轮储能系统在偏心条件下的动能、势能、发电机系统的磁场能以及系统的耗散函数,由Lagrange-Maxwell方程建立磁悬浮飞轮系统和两相四极永磁发电机系统的机电耦合动力学方程.采用数值法对0.6MW磁悬浮飞轮储能系统进行了仿真分析,研究结果表明,系统机电耦合非线性方程存在稳定的与转速同频的基频和三倍频周期运动解,且基频振动幅值比三倍频振动幅值大.对于稳定的磁悬浮储能飞轮机电耦合系统,飞轮转速增大,或磁轴承系统刚度减小或阻尼增大,或磁场能(电枢反应磁场能或永磁励磁磁场能)减小,可使系统的非线性振动幅值减小.而增大磁轴承系统的刚度,或减小磁轴承系统的阻尼,或增大系统的磁场能有可能破坏机电耦合系统的稳定性,使飞轮失稳.     

Input-driven oscillations in networks with excitatory and inhibitory neurons with dynamic synapses

Previous work has shown that networks of neurons with two coupled layers of excitatory and inhibitory neurons can reveal oscillatory activity. For example, B?rgers and Kopell (2003) have shown that oscillations occur when the excitatory neurons receive a sufficiently large input. A constant drive to the excitatory neurons is sufficient for oscillatory activity. Other studies (Doiron, Chacron, Maler, Longtin, & Bastian, 2003; Doiron, Lindner, Longtin, Maler, & Bastian, 2004) have shown that networks of neurons with two coupled layers of excitatory and inhibitory neurons reveal oscillatory activity only if the excitatory neurons receive correlated input, regardless of the amount of excitatory input. In this study, we show that these apparently contradictory results can be explained by the behavior of a single model operating in different regimes of parameter space. Moreover, we show that adding dynamic synapses in the inhibitory feedback loop provides a robust network behavior over a broad range of stimulus intensities, contrary to that of previous models. A remarkable property of the introduction of dynamic synapses is that the activity of the network reveals synchronized oscillatory components in the case of correlated input, but also reflects the temporal behavior of the input signal to the excitatory neurons. This allows the network to encode both the temporal characteristics of the input and the presence of spatial correlations in the input simultaneously.     

Oscillatory synchronization requires precise and balanced feedback inhibition in a model of the insect antennal lobe

In the insect olfactory system, odor-evoked transient synchronization of antennal lobe (AL) projection neurons (PNs) is phase-locked to the oscillations of the local field potential. Sensory information is contained in the spatiotemporal synchronization pattern formed by the identities of the phase-locked PNs. This article investigates the role of feedback inhibition from the local neurons (LNs) in this coding. First, experimental biological results are reproduced with a reduced computational spiking neural network model of the AL. Second, the low complexity of the model leads to a mathematical analysis from which a lower bound on the phase-locking probability is derived. Parameters involved in the bound indicate that PN phase locking depends not only on the number of LN-evoked inhibitory postsynaptic potentials (IPSPs) previously received, but also on their temporal jitter. If the inhibition received by a PN at the current oscillatory cycle is both perfectly balanced (i.e., equal to the mean inhibitory drive) and precise (without any jitter), then the PN will be phase-locked at the next oscillatory cycle with probability one.