Sun Xiaojuan, Perc Matjaz, Lu Qishao, Kurths Jürgen
School of Science, Beihang University, Beijing 100083, China.
Chaos. 2008 Jun;18(2):023102. doi: 10.1063/1.2900402.
Spatial coherence resonance in a spatially extended system that is locally modeled by Hodgkin-Huxley (HH) neurons is studied in this paper. We focus on the ability of additive temporally and spatially uncorrelated Gaussian noise to extract a particular spatial frequency of excitatory waves in the medium, whereby examining the impact of diffusive and small-world network topology that determines the interactions amongst coupled HH neurons. We show that there exists an intermediate noise intensity that is able to extract a characteristic spatial frequency of the system in a resonant manner provided the latter is diffusively coupled, thus indicating the existence of spatial coherence resonance. However, as the diffusive topology of the medium is relaxed via the introduction of shortcut links introducing small-world properties amongst coupled HH neurons, the ability of additive Gaussian noise to evoke ordered excitatory waves deteriorates rather spectacularly, leading to the decoherence of the spatial dynamics and with it related absence of spatial coherence resonance. In particular, already a minute fraction of shortcut links suffices to substantially disrupt coherent pattern formation in the examined system.
本文研究了在由霍奇金-赫胥黎（HH）神经元局部建模的空间扩展系统中的空间相干共振。我们关注加性时间和空间不相关高斯噪声提取介质中特定空间频率的兴奋性波的能力，从而研究扩散和小世界网络拓扑结构对耦合HH神经元之间相互作用的影响。我们表明，存在一个中间噪声强度，只要系统是扩散耦合的，该强度就能以共振方式提取系统的特征空间频率，这表明存在空间相干共振。然而，随着通过引入捷径链接来放松介质的扩散拓扑结构，从而在耦合的HH神经元之间引入小世界特性，加性高斯噪声激发有序兴奋性波的能力会显著恶化，导致空间动力学的退相干以及与之相关的空间相干共振的缺失。特别是，在所研究的系统中，极小比例的捷径链接就足以严重破坏相干模式的形成。
