受噪声和网络结构控制的激励元件
Excitable elements controlled by noise and network structure
摘要：
我们研究随机可兴奋元素、主动旋转子的复杂网络的集体动力学。在无限个单元的热力学极限下，我们对网络应用平均场论，然后用高斯近似得到一个确定性微分方程的封闭集合。这些方程决定了网络的序参量。我们发现，同质网络中每个元素的连接数量的均匀减少只会改变分叉阈值，而不会对网络动态产生质的变化。相反，连接数量的异质性导致可兴奋状态的分叉。特别是，我们表明，噪声强度的临界值的鞍结分岔不断增长的连通性方差下降。相应的临界值的发病全球振荡（霍普夫分岔）显示非单调依赖于结构的异质性，显示在中等连接方差的最小值。
英文摘要：
We study collective dynamics of complex networks of stochastic excitable elements, active rotators. In the thermodynamic limit of infinite number of elements, we apply a mean-field theory for the network and then use a Gaussian approximation to obtain a closed set of deterministic differential equations. These equations govern the order parameters of the network. We find that a uniform decrease in the number of connections per element in a homogeneous network merely shifts the bifurcation thresholds without producing qualitative changes in the network dynamics. In contrast, heterogeneity in the number of connections leads to bifurcations in the excitable regime. In particular we show that a critical value of noise intensity for the saddle-node bifurcation decreases with growing connectivity variance. The corresponding critical values for the onset of global oscillations (Hopf bifurcation) show a non-monotone dependency on the structural heterogeneity, displaying a minimum at moderate connectivity variances.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
