Complex Network Restoration Dynamics Method Considering Continuity between Cascading Failure and Restoration

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

Abstract

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

CLC Number:

O414.2
U113

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.

Figures/Tables 14

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

Fig.2 Continuation curve of cascading failure and restoration process

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

Fig.3 Three-layer traffic complex network

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

Fig.4 State distribution of failure nodes

Fig.5 Network simulation restoration results

Fig.6 Effect of restoration node ratio on restoration degree

Fig.7 Influence of coupling coefficient on restoration effect

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

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

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

Fig.10 Power network restoration process

Fig.11 Biological network restoration process

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