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With the development of network science, the static network has been unable to clearly characterize the dynamic process of the network. In real networks, the interaction between individuals evolves rapidly over time. This network model closely links time to interaction process. Compared with static networks, dynamic networks can clearly describe the interaction time of nodes, which has more practical significance. Therefore, how to better describe the behavior changes of networks after being attacked based on time series is an important problem in the existing cascade failure research. In order to better answer this question, a failure model based on time series is proposed in this paper. The model is constructed according to time, activation ratio, number of edges and connection probability. By randomly attacking nodes at a certain time, the effects of four parameters on sequential networks are analyzed. In order to validate the validity and scientificity of this failure model, we use small social networks in the United States. The experimental results show that the model is feasible. The model takes into account the time as well as the spreading dynamics and provides a reference for explaining the dynamic networks in reality.
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Keywords:
- time series/
- cascading failure/
- robustness
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pactive n m $\langle {k^{ { { {\rm{in} }/{\rm{out} } } } } } \rangle$ 0.1 200 32 0.16 0.2 200 68 0.34 0.3 200 191 0.955 0.5 200 787 3.945 0.6 200 843 4.215 1.0 200 3203 16.015 
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Parameter n m $\langle {k^{ {\text{in} }/{\text{out} } } } \rangle$ M= 1 200 12 0.060 M= 2 200 24 0.120 M= 5 200 143 0.715 M= 8 200 507 2.535 M= 10 200 853 4.265 pcon= 0.1 200 16 0.080 pcon= 0.2 200 45 0.225 pcon= 0.5 200 179 0.895 pcon= 0.6 200 276 1.380 pcon= 1.0 200 983 4.915 DownLoad:
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T n m $\langle {k^{ {\text{in} }/{\text{out} } } } \rangle$ 2 200 57 0.285 5 200 68 0.340 10 200 70 0.350 20 200 81 0.405 30 200 71 0.355 DownLoad:
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T n m $\langle {k^{ {\text{in} }/{\text{out} } } } \rangle$ 2 200 931 4.655 5 200 5258 26.290 10 200 11689 58.445 20 200 15464 77.320 30 200 23062 115.310 DownLoad:
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Source node Target node Time Source node Target node Time Source node Target node Time ${v_1}$ ${v_{12}}$ 4 ${v_3}$ ${v_{13}}$ 2 ${v_{16}}$ ${v_{10}}$ 2 ${v_1}$ ${v_{18}}$ 9 ${v_3}$ ${v_{18}}$ 2 ${v_{16}}$ ${v_{12}}$ 4 ${v_2}$ ${v_{10}}$ 7 ${v_3}$ ${v_{25}}$ 2 ${v_{16}}$ ${v_{14}}$ 2 ${v_2}$ ${v_{12}}$ 1 ${v_4}$ ${v_{10}}$ 4 ${v_{16}}$ ${v_{18}}$ 4 ${v_2}$ ${v_{13}}$ 1 ${v_4}$ ${v_{12}}$ 1 ${v_{16}}$ ${v_{32}}$ 1 ${v_2}$ ${v_{14}}$ 1 ${v_4}$ ${v_{27}}$ 1 ${v_{17}}$ ${v_{10}}$ 3 ${v_2}$ ${v_{18}}$ 1 ${v_4}$ ${v_{32}}$ 4 ${v_{18}}$ ${v_{12}}$ 2 ${v_3}$ ${v_{10}}$ 2 ${v_5}$ ${v_{12}}$ 4 ${v_{18}}$ ${v_{13}}$ 1 ${v_5}$ ${v_{13}}$ 1 ${v_8}$ ${v_{10}}$ 1 ${v_{18}}$ ${v_{14}}$ 2 ${v_5}$ ${v_{18}}$ 5 ${v_8}$ ${v_{12}}$ 2 ${v_{19}}$ ${v_{14}}$ 7 ${v_5}$ ${v_{20}}$ 1 ${v_8}$ ${v_{13}}$ 7 ${v_{21}}$ ${v_{13}}$ 1 ${v_5}$ ${v_{27}}$ 1 ${v_8}$ ${v_{15}}$ 1 ${v_{21}}$ ${v_{20}}$ 4 ${v_7}$ ${v_1}$ 1 ${v_8}$ ${v_{18}}$ 2 ${v_{22}}$ ${v_{10}}$ 3 ${v_7}$ ${v_{18}}$ 1 ${v_8}$ ${v_{20}}$ 2 ${v_{22}}$ ${v_{12}}$ 4 ${v_7}$ ${v_{33}}$ 1 ${v_8}$ ${v_{27}}$ 2 ${v_{22}}$ ${v_{13}}$ 1 ${v_8}$ ${v_2}$ 1 ${v_8}$ ${v_{32}}$ 2 ${v_{22}}$ ${v_{18}}$ 11 ${v_9}$ ${v_1}$ 3 ${v_{11}}$ ${v_{10}}$ 3 ${v_{22}}$ ${v_{27}}$ 3 ${v_9}$ ${v_5}$ 2 ${v_{11}}$ ${v_{12}}$ 1 ${v_{22}}$ ${v_{31}}$ 1 ${v_9}$ ${v_{12}}$ 1 ${v_{11}}$ ${v_{14}}$ 6 ${v_{24}}$ ${v_3}$ 2 ${v_9}$ ${v_{18}}$ 1 ${v_{11}}$ ${v_{18}}$ 1 ${v_{24}}$ ${v_6}$ 1 ${v_9}$ ${v_{33}}$ 2 ${v_{11}}$ ${v_{25}}$ 1 ${v_{24}}$ ${v_{10}}$ 8 ${v_{10}}$ ${v_{12}}$ 1 ${v_{11}}$ ${v_{30}}$ 3 ${v_{24}}$ ${v_{12}}$ 4 ${v_{10}}$ ${v_{13}}$ 1 ${v_{11}}$ ${v_{32}}$ 1 ${v_{24}}$ ${v_{13}}$ 3 ${v_{10}}$ ${v_{18}}$ 2 ${v_{16}}$ ${v_2}$ 1 ${v_{24}}$ ${v_{18}}$ 2 ${v_{24}}$ ${v_{25}}$ 3 ${v_{28}}$ ${v_5}$ 10 ${v_{33}}$ ${v_{10}}$ 2 ${v_{24}}$ ${v_{32}}$ 3 ${v_{28}}$ ${v_{12}}$ 2 ${v_{33}}$ ${v_{14}}$ 2 ${v_{24}}$ ${v_{33}}$ 1 ${v_{28}}$ ${v_{23}}$ 1 ${v_{33}}$ ${v_{25}}$ 1 ${v_{24}}$ ${v_{35}}$ 1 ${v_{29}}$ ${v_3}$ 1 ${v_{34}}$ ${v_{10}}$ 1 ${v_{25}}$ ${v_{10}}$ 1 ${v_{29}}$ ${v_{10}}$ 2 ${v_{34}}$ ${v_{12}}$ 9 ${v_{25}}$ ${v_{12}}$ 5 ${v_{29}}$ ${v_{12}}$ 6 ${v_{34}}$ ${v_{13}}$ 1 ${v_{25}}$ ${v_{14}}$ 4 ${v_{29}}$ ${v_{14}}$ 2 ${v_{34}}$ ${v_{14}}$ 1 ${v_{25}}$ ${v_{18}}$ 2 ${v_{29}}$ ${v_{15}}$ 2 ${v_{34}}$ ${v_{18}}$ 7 ${v_{26}}$ ${v_{10}}$ 3 ${v_{29}}$ ${v_{25}}$ 1 ${v_{34}}$ ${v_{20}}$ 2 ${v_{26}}$ ${v_{12}}$ 1 ${v_{29}}$ ${v_{32}}$ 4 ${v_{35}}$ ${v_2}$ 1 ${v_{26}}$ ${v_{14}}$ 12 ${v_{30}}$ ${v_{13}}$ 1 ${v_{35}}$ ${v_6}$ 1 ${v_{26}}$ ${v_{15}}$ 2 ${v_{30}}$ ${v_{14}}$ 7 ${v_{35}}$ ${v_{10}}$ 2 ${v_{26}}$ ${v_{18}}$ 1 ${v_{31}}$ ${v_{10}}$ 2 ${v_{35}}$ ${v_{12}}$ 2 ${v_{26}}$ ${v_{30}}$ 3 ${v_{31}}$ ${v_{13}}$ 3 ${v_{35}}$ ${v_{13}}$ 1 ${v_{35}}$ ${v_{14}}$ 4 ${v_{35}}$ ${v_{25}}$ 2 ${v_{35}}$ ${v_{32}}$ 3 ${v_{35}}$ ${v_{18}}$ 1 DownLoad:
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