Complete Classification of the Macroscopic Behavior of a Heterogeneous Network of Theta Neurons
Complete Classification of the Macroscopic Behavior of a Heterogeneous Network of Theta Neurons
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DOI：
10.1162/neco_a_00525
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发表时间：
2013-12-01
影响因子：
2.9
通讯作者：
So, Paul
中科院分区：
文献类型：
--
作者：
Luke, Tanushree B.;Barreto, Ernest;So, Paul
我们设计和分析了一个大型网络的theta神经元，这是理想化的I型神经元的动力学。该网络是异质的，因为它包括固有的尖峰和可兴奋的神经元。这种耦合是全局性的，通过可调节锐度的脉冲式突触。使用最近开发的分析方法，我们确定所有可能的渐近状态，可以表现出一个平均场变量，捕捉网络的宏观状态。这些包括两个平衡状态，反映部分同步的网络和一个极限环状态，在网络同步的程度振荡的时间。我们的方法还允许一个完整的分叉分析，我们进行的参数，捕捉神经元的兴奋性程度，在人口中的异质性，耦合强度（可以是兴奋性或抑制性）。我们发现，当神经元的内在动力学和网络相互作用相互加强时，网络通常倾向于两个宏观平衡状态。相反，当这些网络特征之间存在竞争时，则容易出现极限环状态、分叉和多稳定性。最后，我们表明，我们的结果表现出有限的网络实现合理的大小。
We design and analyze the dynamics of a large network of theta neurons, which are idealized type I neurons. The network is heterogeneous in that it includes both inherently spiking and excitable neurons. The coupling is global, via pulselike synapses of adjustable sharpness. Using recently developed analytical methods, we identify all possible asymptotic states that can be exhibited by a mean field variable that captures the network's macroscopic state. These consist of two equilibrium states that reflect partial synchronization in the network and a limit cycle state in which the degree of network synchronization oscillates in time. Our approach also permits a complete bifurcation analysis, which we carry out with respect to parameters that capture the degree of excitability of the neurons, the heterogeneity in the population, and the coupling strength (which can be excitatory or inhibitory). We find that the network typically tends toward the two macroscopic equilibrium states when the neuron's intrinsic dynamics and the network interactions reinforce one another. In contrast, the limit cycle state, bifurcations, and multistability tend to occur when there is competition among these network features. Finally, we show that our results are exhibited by finite network realizations of reasonable size.