识别对多稳定网络的动态鲁棒性至关重要的节点特性
Identifying nodal properties that are crucial for the dynamical robustness of multi-stable networks
摘要：
我们研究了连接在不同网络拓扑结构中的双稳态元素的集体动力学，从环和小世界网络到无标度网络和恒星。我们估计这样的网络的动态鲁棒性，通过引入多节点流域稳定性的概念的一个变体，这使我们能够衡量的全球稳定性的动态网络响应于局部扰动影响某一类节点的系统。我们发现，扰动节点具有高的接近度和中间中心显着降低了系统的能力，以返回到所需的状态。这种效应对于星形网络非常明显，其中一个中心节点的接近度/中间中心度与所有外围节点显著不同。在这样的网络中，单个枢纽节点的扰动有能力破坏集体状态。另一方面，即使大多数外围节点受到强烈扰动，枢纽节点也能设法将系统恢复到原始状态，这表明受扰动节点的中心性对网络动态的巨大影响。此外，我们探索探索双稳态动力学元素的随机无标度网络。我们利用m=1和m=2的随机无标度网络中节点的介数中心性、贴近度中心性和度分布的差异，来探讨在这些异构网络中，哪种中心性属性对集体动力学的鲁棒性影响最大.值得注意的是，我们发现明确的证据表明，扰动节点的介数中心性是更重要的动态鲁棒性，比接近中心性或程度的节点。这一结果对于决定保护哪些节点以维护该网络的集体状态以对抗有针对性的本地化攻击非常重要。
英文摘要：
We investigate the collective dynamics of bi-stable elements connected in different network topologies, ranging from rings and small-world networks, to scale-free networks and stars. We estimate the dynamical robustness of such networks by introducing a variant of the concept of multi-node basin stability, which allows us to gauge the global stability of the dynamics of the network in response to local perturbations affecting a certain class of nodes of a system. We show that perturbing nodes with high closeness and betweeness-centrality significantly reduces the capacity of the system to return to the desired state. This effect is very pronounced for a star network which has one hub node with significantly different closeness/betweeness-centrality than all the peripheral nodes. In such a network, perturbation of the single hub node has the capacity to destroy the collective state. On the other hand, even when a majority of the peripheral nodes are strongly perturbed, the hub manages to restore the system to its original state, demonstrating the drastic effect of the centrality of the perturbed node on the dynamics of the network. Further, we explore explore Random Scale-Free Networks of bi-stable dynamical elements. We exploit the difference in the distribution of betweeness centralities, closeness centralities and degrees of the nodes in Random Scale-Free Networks with m=1 and m=2, to probe which centrality property most influences the robustness of the collective dynamics in these heterogeneous networks. Significantly, we find clear evidence that the betweeness centrality of the perturbed node is more crucial for dynamical robustness, than closeness centrality or degree of the node. This result is important in deciding which nodes to safeguard in order to maintain the collective state of this network against targeted localized attacks.
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