A unified dynamic scaling property for the unified hybrid network theory framework

Abstract

In this article, we present a new type of unified dynamic scaling property for synchronizability, which can describe the scaling relationship between dynamic synchronizability and four hybrid ratios under the unified hybrid network theory framework (UHNTF). Our theory results can not only be applied to judge and analyze dynamic synchronizability for most of complex networks associated with the UHNTF, but also we can flexibly adjust and design different hybrid ratios and scaling exponent to meet actual requirement for the dynamic characteristics of the UHNTF.

Graphical abstract

Keywords

dynamic scaling property / unified hybrid network theory framework (UHNTF) / synchronizability / hybrid ratios

References

[1] D. J. Watts, Small Worlds: The Dynamics of Networks Between Order and Randomness, Princeton: Princeton University Press, 1999

[2] L. M. Pecora and T. C. Carroll, Driving systems with chaotic signals, Phys. Rev. A, 1993, 44(4): 2374

[3] L. M. Pecora and T. C. Carroll, Master Stability functions for synchronized coupled systems, Phys. Rev. Lett., 1998, 80(10): 2109

[4] K. Park, L. Huang, and Y. C. Lai, Desynchronization waves in small-world networks, Phys. Rev. E, 2007, 75(2): 026211

[5] C. Y. Yin, B. H. Wang, W. X. Wang, and G. R. Chen, Geographical effect on small-world network synchronization, Phys. Rev. E, 2008, 77(2): 027102

[6] L. K. Tang, J. A. Lu, and G. R. Chen, Synchronizability of small-world networks generated from ring networks with equal-distance edge additions, Chaos, 2012, 22(2): 023121

[7] D. J. Watts and S. H. Strogatz, Collective dynamics of small world networks, Nature, 1998, 393: 440

[8] A. L. Barabási and R. Albert, Emergence of scaling in random networks, Science, 1999, 286(5439): 509

[9] J. H. Lü, X. H. Yu, G. R. Chen, and D. Z. Chen, Characterizing the synchronizability of small-world dynamical networks, IEEE Trans. Circuits Syst. I, 2004, 51(1): 787

[10] K. Kaneko, Coupled Map Lattices, Singapore: World Scientific, 1992

[11] S. C. Manrubia and S. M. Mikhailov, Mutual synchronization and clustering in randomly coupled chaotic dynamical networks, Phys. Rev. E, 1999, 60(2): 1579

[12] X. F. Wang and G. R. Chen, Synchronization in small-world dynamical networks, Int. J. Bifurcation Chaos, 2002, 12(1): 187

[13] X. F. Wang and G. R. Chen, Synchronization in scale-free dynamical networks: robustness and fragility, IEEE Trans. Circuits Syst. I, 2002, 49(1): 54

[14] A. E. Motter, C. S. Zhou, and J. Kurths, Network synchronization, diffusion, and the paradox of heterogeneity, Phys. Rev. E, 2005, 71(1): 016116

[15] T. Zhou, M. Zhao, and B. H. Wang, Better synchronizability predicted by crossed double cycle, Phys. Rev. E, 2006, 73(3): 037101

[16] X. Wu, B. H. Wang, T. Zhou, W. X. Wang, M. Zhao, and H. J. Yang, The synchronizability of highly clustered scale-free networks, Chin. Phys. Lett., 2006, 23(4): 1046

[17] J. Q. Fang and Y. Liang, Topological Properties and transition features generated by a new hybrid preferential model, Chin. Phys. Lett., 2005, 22(10): 2719

[18] J. Q. Fang, Q. Bi, and Y. Li, Toward a harmonious unifying hybrid model for any evolving complex networks, Adv. Comp. Syst., 2007, 10(2): 117

[19] J. Q. Fang, Q. Bi, Y. Li, and Q. Liu, A harmonious unifying hybrid preferential model of complex dynamic networks and its universal characteristics, Sci. China Ser. G, 2007, 37(2): 230

[20] J. Q. Fang, Q. Bi, Y. Li, and Q. Liu, Sensitivity of exponents of three-power-laws to hybrid ratio in weighted HUHPM, Chin. Phys. Lett., 2007, 24(1): 279

[21] X. B. Lu, X. F. Wang, X. Li, and J. Q. Fang, Synchronization in weighted complex networks: Heterogeneity and synchronizability, Physica A, 2006, 370(2): 381

[22] J. Q. Fang, Q. Bi, Y. Li, and Q. Liu, A harmonious unifying hybrid preferential model and its universal properties for complex dynamical networks, Sci. China Ser. G, 2007, 50(3): 379

[23] Y. Li, J. Q. Fang, Q. Bi, and Q. Liu, Entropy characteristic on harmonious unifying hybrid preferential networks, Entropy, 2007, 9(2): 73

[24] Q. Bi and J. Q Fang, Entropy and HUHPM approach for complex networks, Physica A, 2007, 383(2): 753

[25] J. Q. Fang, Q. Bi, and Y. Li, From a harmonious unifying hybrid preferential model toward a large unifying hybrid network model, Int. J. Mod. Phys. B, 2007, 21(30): 5121

[26] J. Q. Fang, Q. Bi, and Y. Li, Advances in theoretical models of network science, Front. Phys. China, 2007, 1(2): 109

[27] J. Q. Fang, Exploring theoretical model of network science and research progresses, Science Technology Review, 2006, 24(12): 67 (in Chinese)

[28] J. Q. Fang, Advances in the research of dynamical complexity of nonlinear network, Prog. Nat. Sci., 2007, 17(9): 841(in Chinese)

[29] J. Q. Fang, X. F. Wang, Z. G. Zheng, Z. R. Di, and Y. Fang, New interdisciplinary science: Network science (I), Prog. Phys., 2007, 27(3): 239(in Chinese)

[30] J. Q. Fang, Theoretical research progress in complexity of complex dynamical networks, Prog. Nat. Sci., 2007, 17(7): 761(in Chinese)

[31] X. B. Lu, X. F. Wang, and J. Q. Fang, Topological transition features and synchronizability of a weighted hybrid preferential network, Physica A, 2006, 371(2): 841

[32] J. Q. Fang, Network complexity pyramid with five levels, Int. J. Syst. Cont. Commun., 2009, 1(4): 453

[33] J. Q. Fang, Mastering Chaos and Developing High-Tech, Beijing: Atomic Energy Press, 2002

[34] J. Q. Fang and Y. Li, Advances in unified hybrid theoretical model of network science, Adv. Mech., 2008, 38(6): 663

[35] J. Q. Fang and Y. Li, Transition features from simplicity-universality to complexity-diversification under the UHNMVSG, Commun. Theor. Phys., 2010, 53(2): 389

[36] J. Q. Fang, Y. Li, and Q. Liu, Three Types of Network Complexity Pyramid, (book: Advances in Network Complexity), Berlin: Wiley-VCH, 2012

[37] Y. Li, J. Q. Fang, Q. Liu, and Q. Bi, Exploring the characteristics of Chinese high technology industry networks, J. Univ. Shanghai Sci. Tech., 2008, 30(3): 300(in Chinese)

[38] Q. Liu, J. Q. Fang, and Y. Li, Several features of China Top-100 electronic information technology enterprise network, J. Guangxi Norm. Univ., 2008, 26(4): 1(in Chinese)

[39] J. Q. Fang, Investigating high-tech networks with four levels from developing viewpoint of network science, World Sci.-Tech. R&D, 2008, 30(5): 667(in Chinese)

[40] Y. Li, J. Q. Fang, and Q. Liu, Characteristics of continuum percolation evolving network, Comp. Syst. Comp. Sci., 2010, 7(2): 97(in Chinese)

[41] Y. Li, J. Q. Fang, and Q. Liu, Global nuclear plant network and its characteristics, Atomic Energy Science and Technology, 2010, 44(9): 1139(in Chinese)

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg