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Identifying convergent speed is an important but rarely discussed problem in estimating topologies of complex networks. In this paper, we discuss this problem mainly in both weakly and strongly coupled conditions. In the weakly coupled conditions, the convergent speed we defined increases linearly with coupling strength increasing. After analyzing the dynamics, we find that this relation is universal. In light of the repeatedly driving method we proposed recently, we generalize the definition of the convergent speed into the area of synchronization. In this case, there is a best length of the driving time series to maximize the convergent speed. The knowledge of convergent speed helps us understand the topological information embedded in the time series.
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Keywords:
- complex network /
- estimate topology /
- adaptive-feedback /
- convergent speed
[1] Lu J A 2010 Complex Systems and Complexity Science 7 19 (in Chinese) [陆君安 2010 复杂系统与复杂性科学 7 19]
[2] Yu D, Righero M, Vicente P 2006 Phys. Rev. Lett. 96 114102
[3] Timme M 2007 Phys. Rev. Lett. 98 224101
[4] Ren j, Wang W X, Li B, Lai Y C 2010 Phys. Rev. Lett. 104 058701
[5] Liang X M, Liu Z H, Li B W 2009 Phys. Rev. E 80 046102
[6] Bu S L, Jiang I M 2008 Europhys. Lett. 82 68001
[7] Liang X Liu Z, Li B 2009 Phys.Rev. E 80 046102
[8] Shen Y, Hou Z, Xin H 2010 Chaos 20 013110
[9] Chen L, Lu J A, Tse C K 2009 IEEE Trans. Circuits Syst. II- Express Briefs 56 310
[10] Sun F, Peng H P, Xiao J H 2012 Nonlinear Dyn 67 1457
[11] Huang L, Chen Q F, Lai Y C, Pecora L M 2009 Phys. Rev. E 80 036204
[12] Lorenz E N, Atmos J 1963 Sci. 20 130
[13] Rössler O E 1976 Phys. Lett. A 57 397
[14] Chen G, Ueta T 1999 Int. J. Bifurcation Chaos Appl. Sci. Eng. 9 1465
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[1] Lu J A 2010 Complex Systems and Complexity Science 7 19 (in Chinese) [陆君安 2010 复杂系统与复杂性科学 7 19]
[2] Yu D, Righero M, Vicente P 2006 Phys. Rev. Lett. 96 114102
[3] Timme M 2007 Phys. Rev. Lett. 98 224101
[4] Ren j, Wang W X, Li B, Lai Y C 2010 Phys. Rev. Lett. 104 058701
[5] Liang X M, Liu Z H, Li B W 2009 Phys. Rev. E 80 046102
[6] Bu S L, Jiang I M 2008 Europhys. Lett. 82 68001
[7] Liang X Liu Z, Li B 2009 Phys.Rev. E 80 046102
[8] Shen Y, Hou Z, Xin H 2010 Chaos 20 013110
[9] Chen L, Lu J A, Tse C K 2009 IEEE Trans. Circuits Syst. II- Express Briefs 56 310
[10] Sun F, Peng H P, Xiao J H 2012 Nonlinear Dyn 67 1457
[11] Huang L, Chen Q F, Lai Y C, Pecora L M 2009 Phys. Rev. E 80 036204
[12] Lorenz E N, Atmos J 1963 Sci. 20 130
[13] Rössler O E 1976 Phys. Lett. A 57 397
[14] Chen G, Ueta T 1999 Int. J. Bifurcation Chaos Appl. Sci. Eng. 9 1465
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