Role of long cycles in excitable dynamics on graphs.
Role of long cycles in excitable dynamics on graphs.
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DOI：
10.1103/physreve.90.052805
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发表时间：
2014-11
期刊：
影响因子：
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通讯作者：
Guadalupe C. Garcia;A. Lesne;C. Hilgetag;M. Hütt
中科院分区：
文献类型：
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作者：
Guadalupe C. Garcia;A. Lesne;C. Hilgetag;M. Hütt
可兴奋网络中的拓扑循环在维持网络活动方面可以发挥重要作用。当正确激活时，循环充当动态起搏器，维持整个网络的活动。之前的大多数研究都集中在短周期对网络动态的贡献上。在这里，我们确定了稀疏随机图中不同激活运行期间使用的特定循环，作为表征任何长度循环的贡献的基础。模拟和改进的平均场方法都证明，当周期长度增加时，周期使用量会减少，这反映了激励后恢复时间长和对异相外部激励的低脆弱性之间的权衡。尽管有这种统计观察，我们发现长周期的成功使用虽然很少见，但对于维持网络活动具有重要的功能后果：平均周期长度是影响网络中活动的平均生命周期的周期长度分布的主要特征。特别是，使用长循环而不是短循环与更高的寿命相关，并且在长循环中缩短捷径往往会增加活动的平均寿命。因此，我们的研究结果强调了长周期在维持网络活动方面所发挥的重要作用，这一作用之前被低估了。在更一般的层面上，这些发现强调了网络拓扑，特别是循环结构对于自我维持的网络动态的重要性。
Topological cycles in excitable networks can play an important role in maintaining the network activity. When properly activated, cycles act as dynamic pacemakers, sustaining the activity of the whole network. Most previous research has focused on the contributions of short cycles to network dynamics. Here, we identify the specific cycles that are used during different runs of activation in sparse random graphs, as a basis of characterizing the contribution of cycles of any length. Both simulation and a refined mean-field approach evidence a decrease in the cycle usage when the cycle length increases, reflecting a trade-off between long time for recovery after excitation and low vulnerability to out-of-phase external excitations. In spite of this statistical observation, we find that the successful usage of long cycles, though rare, has important functional consequences for sustaining network activity: The average cycle length is the main feature of the cycle length distribution that affects the average lifetime of activity in the network. Particularly, use of long, rather than short, cycles correlates with higher lifetime, and cutting shortcuts in long cycles tends to increase the average lifetime of the activity. Our findings, thus, emphasize the essential, previously underrated role of long cycles in sustaining network activity. On a more general level, the findings underline the importance of network topology, particularly cycle structure, for self-sustained network dynamics.