Pinning control of scale-free dynamical networks. (English) Zbl 0995.90008

Summary: Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions have the power-law form. In the present work, control of a scale-free dynamical network by applying local feedback injections to a fraction of network nodes is investigated. The specifically and randomly pinning schemes are considered. The specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme. The method is applied to an array of Chua’s oscillators as an example.


90B10 Deterministic network models in operations research
Full Text: DOI


[1] K. Kaneko (Ed.), Coupled Map Lattices, World Scientific Pub. Co., Singapore, 1992.; K. Kaneko (Ed.), Coupled Map Lattices, World Scientific Pub. Co., Singapore, 1992. · Zbl 1055.37540
[2] L.O. Chua (Ed.), IEEE Trans. Circuits Syst. 42 (1995) 557.; L.O. Chua (Ed.), IEEE Trans. Circuits Syst. 42 (1995) 557.
[3] Strogatz, S. H., Nature, 410, 268 (2001)
[4] Faloutsos, M.; Faloutsos, P.; Faloutsos, C., Comput. Commun. Rev., 29, 251 (1999)
[5] Albert, R.; Jeong, H.; Barabási, A.-L., Nature, 401, 130 (1999)
[6] Williams, R. J.; Martinez, N. D., Nature, 404, 180 (2000)
[7] Jeong, H.; Tombor, B.; Albert, R.; Oltvai, Z.; Barabási, A.-L., Nature, 407, 651 (2000)
[8] Newman, M. E.J., Proc. Natl. Acad. Sci., 98, 404 (2001)
[9] Wassrman, S.; Faust, K., Social Network Analysis (1994), Cambridge University Press: Cambridge University Press Cambridge
[10] Erdos, P.; Renyi, A., Publ. Math. Inst. Hung. Acad. Sci., 5, 17 (1960)
[11] Watts, D. J.; Strogatz, S. H., Nature, 393, 440 (1998)
[12] Barabási, A.-L.; Albert, R., Science, 286, 509 (1999)
[13] Barabási, A.-L.; Albert, R.; Jeong, H., Physica A, 272, 173 (1999)
[14] Albert, R.; Jeong, H.; Barabási, A.-L., Nature, 406, 387 (2000)
[15] Callway, D. S.; Newman, M. E.J.; Strogatz, S. H.; Watts, D. J., Phys. Rev. Lett., 85, 5468 (2000)
[16] Cohen, R.; Erez, K.; Ben-Avraham, D.; Havlin, S., Phys. Rev. Lett., 85, 4626 (2000)
[17] Wang, X. F.; Chen, G., IEEE Trans. Circuits Syst. I, 49, 54 (2002)
[18] Hu, G.; Qu, Z., Phys. Rev. Lett., 72, 68 (1994)
[19] Grigoriev, R. O.; Cross, M. C.; Schuster, H. G., Phys. Rev. Lett., 79, 2795 (1997)
[20] Hu, G., Phys. Rev. E, 62, 3943 (2000)
[21] Albert, R.; Barabási, A.-L., Phys. Rev. Lett., 85, 5234 (2000)
[22] Chua, L. O.; Wu, C. W.; Huang, A.; Zhong, G. Q., IEEE Trans. Circuits Syst., 40, 732 (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.