Asynchronous states and the emergence of synchrony in large networks of interacting excitatory and inhibitory neurons
Asynchronous states and the emergence of synchrony in large networks of interacting excitatory and inhibitory neurons
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DOI：
10.1162/089976603321043685
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发表时间：
2003-01-01
影响因子：
2.9
通讯作者：
Mato, G
中科院分区：
文献类型：
--
作者：
Hansel, D;Mato, G
我们从理论上研究了同步活动在大型网络中出现的条件，该网络由两个广泛连接的神经元组成，一个是兴奋性的，一个是抑制性的。神经元用二次积分-火动力学建模，这为一大类神经元的阈下行为提供了一个很好的近似。除了它们的突触循环输入外，神经元还接受一个强直的外部输入，这个输入在神经元之间是不同的。由于该模型相对简单，可以对其进行分析研究。在给定两个种群的平均发射率的情况下，研究了网络异步状态的稳定性。首先，我们证明即使突触耦合很强，AS也能保持稳定。然后我们研究这种状态可以不稳定的条件。我们展示了这可以通过四种一般方式发生。第一种是鞍节点分叉，它导致另一种平均发射率不同的状态。这种分叉，发生在足够强的反复激发，不对应于同步的出现。相反，在其他三种不稳定机制中，Hopf分岔，对应于振荡同步活动的出现，发生。我们表明，这些机制可以通过它们产生的放电模式以及它们对抑制神经元相互作用和两个种群之间串扰的依赖来区分。我们还证明了除了这些余维1分岔外，系统还可以显示几种余维2分岔：Takens-Bogdanov分岔、Gavrielov-Guckenheimer分岔和双Hopf分岔。
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.