网络拓扑、传输延迟和不应性对耦合可激系统对随机刺激响应的影响
Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus
摘要：
本文研究了耦合离散可激系统网络对外界随机刺激的响应与网络拓扑结构的关系。我们扩展最近的结果，其特征在于响应的光谱特性的邻接矩阵，允许分布在传输延迟和耐火状态的数量，并通过开发一个非微扰近似的稳态网络响应。我们证实了我们的理论结果与数值模拟。我们发现，稳态响应幅度是成反比的持续时间的不应期，这降低了最大可达到的动态范围。我们还发现，传输延迟改变达到稳态所需的时间。重要的是，延迟和不应性都不影响一般预测，即当邻接矩阵的最大特征值为1时，临界和最大动态范围发生。
英文摘要：
We study the effects of network topology on the response of networks of coupled discrete excitable systems to an external stochastic stimulus. We extend recent results that characterize the response in terms of spectral properties of the adjacency matrix by allowing distributions in the transmission delays and in the number of refractory states, and by developing a nonperturbative approximation to the steady state network response. We confirm our theoretical results with numerical simulations. We find that the steady state response amplitude is inversely proportional to the duration of refractoriness, which reduces the maximum attainable dynamic range. We also find that transmission delays alter the time required to reach steady state. Importantly, neither delays nor refractoriness impact the general prediction that criticality and maximum dynamic range occur when the largest eigenvalue of the adjacency matrix is unity.
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