Clustering in small networks of excitatory neurons with heterogeneous coupling strengths
Clustering in small networks of excitatory neurons with heterogeneous coupling strengths
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DOI：
10.1023/a:1021902717424
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发表时间：
2003-03-01
影响因子：
1.2
通讯作者：
Miura, R
中科院分区：
文献类型：
--
作者：
Li, YX;Wang, YQ;Miura, R
具有缓慢上升时间的兴奋性耦合使耦合神经元之间的同步不稳定。因此，在兴奋性神经元网络中，完全同步状态通常是不稳定的。在存在噪声的兴奋性网络的数值研究中，也发现相簇状态（其中神经元被分成多个同步簇）不稳定。问题是，在通过缓慢的兴奋性突触耦合的神经元网络中，同步是否可能。在本文中，我们表明，强大的，同步集群状态可以发生在这样的网络。耦合强度的非均匀分布的影响进行了探讨。解析推导出了聚集态的存在性和稳定性条件。分析表明，如果不同簇中的神经元之间的整体相互作用稳定且足够强以抵消每个簇中神经元之间的不稳定相互作用，则多簇状态在兴奋性网络中可以是稳定的。当耦合强度的异质性加强了稳定的簇间相互作用和/或削弱了不稳定的簇内相互作用时，在所有已知模型神经元的兴奋性网络中都可能出现鲁棒的簇状态。进行了数值模拟，以支持分析结果。
Excitatory coupling with a slow rise time destabilizes synchrony between coupled neurons. Thus, the fully synchronous state is usually unstable in networks of excitatory neurons. Phase-clustered states, in which neurons are divided into multiple synchronized clusters, have also been found unstable in numerical studies of excitatory networks in the presence of noise. The question arises as to whether synchrony is possible in networks of neurons coupled through slow, excitatory synapses. In this paper, we show that robust, synchronous clustered states can occur in such networks. The effects of non-uniform distributions of coupling strengths are explored. Conditions for the existence and stability of clustered states are derived analytically. The analysis shows that a multi-cluster state can be stable in excitatory networks if the overall interactions between neurons in different clusters are stabilizing and strong enough to counter-act the destabilizing interactions between neurons within each cluster. When heterogeneity in the coupling strengths strengthens the stabilizing inter-cluster interactions and/or weakens the destabilizing in-cluster interactions, robust clustered states can occur in excitatory networks of all known model neurons. Numerical simulations were carried out to support the analytical results.