School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Science), Jinan, Shandong Province 250353, China.
State Key Laboratory of Cognitive Neuroscience and Learning IDG/McGovern Institute for Brain & Research, Beijing Normal University, Beijing 100875, China.
Phys Rev E. 2019 Aug;100(2-1):022318. doi: 10.1103/PhysRevE.100.022318.
Edge dynamics is relevant to various real-world systems with complex network topological features. An edge dynamical system is controllable if it can be driven from any initial state to any desired state in finite time with appropriate control inputs. Here a framework is proposed to study the impact of correlation between in- and out-degrees on controlling the edge dynamics in complex networks. We use the maximum matching and direct acquisition methods to determine the controllability limit, i.e., the limit of acceptable change of the edge controllability by adjusting the degree correlation only. Applying the framework to plenty complex networks, we find that the controllability limits are ubiquitous in model and real networks. Arbitrary edge controllability in between the limits can be achieved by properly adjusting the degree correlation. Moreover, a nonsmooth phenomenon occurs in the upper limits, and exponential and power-law scaling behaviors are widespread in the approach or separation speed between the upper and lower limits.
边缘动态与具有复杂网络拓扑特征的各种真实世界系统相关。如果边缘动态系统可以在有限时间内通过适当的控制输入从任何初始状态驱动到任何期望状态，则该系统是可控的。本文提出了一种研究内、外度数之间相关性对复杂网络中边缘动态控制影响的框架。我们使用最大匹配和直接获取方法来确定可控性极限，即仅通过调整度相关性来接受边缘可控性变化的极限。将该框架应用于大量复杂网络，我们发现可控性极限在模型和真实网络中普遍存在。通过适当调整度相关性，可以实现任意介于极限之间的边缘可控性。此外，在上限处出现非平滑现象，并且在上限和下限之间的接近或分离速度中普遍存在指数和幂律缩放行为。
