考虑级联失效与恢复接续性的复杂网络恢复动力学

doi:10.19596/j.cnki.1001-246x.8677

摘要/Abstract

摘要：

为帮助网络系统在级联失效后尽快以合理投入实现恢复, 采用耦合映象格子作为恢复动力学模型基础, 将级联失效作用下的失效状态、耦合系数等作为恢复动力学输入, 建模过程中添加外部恢复力及内部耦合作用形成恢复动力学方法, 与未考虑接续性的3组网络恢复方法相比, 恢复效果分别提升了46.7%、47.9%和66.7%。在6组不同网络上的仿真实验结果表明: 本方法能拟合现实恢复场景, 并能克服网络在层级、规模、建网方法等方面的差异; 在三层交通网络中, 初始恢复比例对恢复程度的边际贡献率可达26.8%, 恢复耦合系数为0.5且首次恢复10%的节点时, 网络恢复程度最高达到86.4%;该恢复动力学方法可有效刻画多种网络的恢复行为。

关键词: 复杂网络, 级联动力学, 耦合映象格子, Henon映射

Abstract:

To help the network system restore with reasonable investment as soon as possible after cascading failure, using coupling map lattice as the basis of the restoration dynamics model, and the failure state and coupling coefficient under the cascade failure are taken as the input of the restoration dynamics. By further adding the external restoring force and the internal coupling to form the restoration dynamics method. The restoration effect is improved by 46.7%, 47.9% and 66.7% respectively compared with three groups of network restoration methods without considering continuity. In addition, the simulation results on six different networks show that this method can fit the real restoration scene, overcome the differences in network level, scale, network construction methods and so on. Specifically, in the three-layer transportation network, the marginal contribution rate of the initial restoration ratio to the restoration degree is 26.8%, and when the coupling coefficient of restoration is 0.5 and 10% of the nodes are restored for the first time, the restoration degree of the network is as high as 86.4%. The proposed restoration dynamics method can effectively describe the restoration process of various networks.

Key words: complex network, cascade dynamics, coupled map lattice, Henon mapping

中图分类号:

O414.2
U113

朱璋元, 王秋玲. 考虑级联失效与恢复接续性的复杂网络恢复动力学[J]. 计算物理, 2024, 41(2): 258-267.

Zhangyuan ZHU, Qiuling WANG. Complex Network Restoration Dynamics Method Considering Continuity between Cascading Failure and Restoration[J]. Chinese Journal of Computational Physics, 2024, 41(2): 258-267.

图/表 14

图1 失效网络的恢复动力学过程(a)失效稳定；(b)恢复开始；(c)恢复进行；(d)恢复结束

Fig.1 Dynamic process of network restoration from failure (a) stable failure state; (b) start of restoration; (c) process of restoration; (d) end of restoration

图2 级联失效与恢复过程的接续关系曲线

Fig.2 Continuation curve of cascading failure and restoration process

表1 对照实验结果

Table 1 Comparative experimental results

网络属性	方法	RL值
节点数=500 平均度=4	本文	2.43
节点数=500 平均度=4	Ref.[14]	4.56

节点数=1 000 平均度=6	本文	2.49
	Ref.[12]	4.78
	Ref.[20]	7.48

图3 三层交通复杂网络

Fig.3 Three-layer traffic complex network

表2 初始参数设置

Table 2 Initial parameter setting

参数	符号	取值
节点初始状态	x_i(t₀)	0.7
结构耦合系数	ε₁	0.3
失效仿真步长	c₁	100
指标比例系数	ω₁	0.5
恢复节点比例	o	10%
恢复耦合系数	ε_r	0.3
时间容忍度	T₁	3
恢复仿真步长	c₂	100

图4 失效节点状态分布

Fig.4 State distribution of failure nodes

图5 网络恢复仿真效果与实际结果

Fig.5 Network simulation restoration results

图6 恢复节点比例对恢复程度的影响

Fig.6 Effect of restoration node ratio on restoration degree

图7 耦合系数对恢复效果的影响

Fig.7 Influence of coupling coefficient on restoration effect

表3 网络拓扑参数

Table 3 Network topology parameters

网络编号	节点数	连边数	平均度	平均聚类系数
①	356	10 657	29.935	0.56
②	90	488	5.422	0.25
③	92	1 554	16.891	0.54

图8 实验2交通网络可视化 (a) 网络①；(b) 网络②；(c) 网络③

Fig.8 Visualization of traffic network (a) Network ①; (b) Network ②; (c) Network ③

图9 初始恢复比例与恢复耦合系数变化关系 (a)网络①；(b)网络②；(c)网络③

Fig.9 Relationship between initial restoration ratio and restoration coupling coefficient (a) Network ①; (b) Network ②; (c) Network ③

图10 电力网络恢复过程

Fig.10 Power network restoration process

图11 生物网络恢复过程

Fig.11 Biological network restoration process

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