Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


Preferences help
enabled [disable] Abstract
Number of results

Journal

2013 | 11 | 6 | 813-823

Article title

Robust projective outer synchronization of coupled uncertain fractional-order complex networks

Content

Title variants

Languages of publication

EN

Abstracts

EN
In this work, we propose a novel projective outer synchronization (POS) between unidirectionally coupled uncertain fractional-order complex networks through scalar transmitted signals. Based on the state observer theory, a control law is designed and some criteria are given in terms of linear matrix inequalities which guarantee global robust POS between such networks. Interestingly, in the POS regime, we show that different choices of scaling factor give rise to different outer synchrony, with various special cases including complete outer synchrony, anti-outer synchrony and even a state of amplitude death. Furthermore, it is demonstrated that although stability of POS is irrelevant to the inner-coupling strength, it will affect the convergence speed of POS. In particular, stronger inner synchronization can induce faster POS. The effectiveness of our method is revealed by numerical simulations on fractional-order complex networks with small-world communication topology.

Publisher

Journal

Year

Volume

11

Issue

6

Pages

813-823

Physical description

Dates

published
1 - 6 - 2013
online
9 - 10 - 2013

Contributors

author
author
  • Faculty of Automation, Guangdong University of Technology, Guangzhou, 510006, China

References

  • [1] R. Albert, A. L. Barabási, Rev. Mod. Phys. 74, 47 (2002) http://dx.doi.org/10.1103/RevModPhys.74.47[Crossref]
  • [2] X. F. Wang, G. Chen, IEEE Circuits Syst. Mag. 3, 6 (2003) http://dx.doi.org/10.1109/MCAS.2003.1228503[Crossref]
  • [3] M. E. J. Newman, Networks: An Introduction (Oxford University Press, New York, 2010) http://dx.doi.org/10.1093/acprof:oso/9780199206650.001.0001[Crossref]
  • [4] D. J. Watts, S. H. Strogatz, Nature 393, 440 (1998) http://dx.doi.org/10.1038/30918[Crossref]
  • [5] A.-L. Barabási, R. Albert, Science 286, 509 (1999) http://dx.doi.org/10.1126/science.286.5439.509[Crossref]
  • [6] G. Palla, I. Derényi, I. Farkas, T. Vicsek, Nature 435, 814 (2005) http://dx.doi.org/10.1038/nature03607[Crossref]
  • [7] A. Clauset, C. Moore, M. E. J. Newman, Nature 453, 98 (2008) http://dx.doi.org/10.1038/nature06830[Crossref]
  • [8] M. E. J. Newman, SIAM Rev. 45, 167 (2003) http://dx.doi.org/10.1137/S003614450342480[Crossref]
  • [9] S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 424, 175 (2006) http://dx.doi.org/10.1016/j.physrep.2005.10.009[Crossref]
  • [10] A. Balanov, N. Janson, D. Postnov, O. Sosnovtseva, Synchronization: From Simple to Complex (Springer-Verlag, Berlin, 2010)
  • [11] A. C. Liu et al., Cell 129, 605 (2007) http://dx.doi.org/10.1016/j.cell.2007.02.047[Crossref]
  • [12] A. K. Engel, P. König, A. K. Kreiter, W. Singer, Science 252, 1177 (1991) http://dx.doi.org/10.1126/science.252.5009.1177[Crossref]
  • [13] X. Li, G. Chen, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 50, 1381 (2003) http://dx.doi.org/10.1109/TCSI.2003.818611[Crossref]
  • [14] A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, C. Zhou, Phys. Rep. 469, 93 (2008) http://dx.doi.org/10.1016/j.physrep.2008.09.002[Crossref]
  • [15] C. P. Li, W. G. Sun, J. Kurths, Phys. Rev. E 76, 046204 (2007) http://dx.doi.org/10.1103/PhysRevE.76.046204[Crossref]
  • [16] C. P. Li, C. X. Xu, W. G. Sun, J. Xu, J. Kurths, Chaos 19, 013106 (2009) http://dx.doi.org/10.1063/1.3068357[Crossref]
  • [17] J. Lü, G. Chen, IEEE Trans. Autom. Control 50, 841 (2005) http://dx.doi.org/10.1109/TAC.2005.849233[Crossref]
  • [18] S. Sarkar, P. Parmananda, Chaos 20, 043108 (2010) http://dx.doi.org/10.1063/1.3496399[Crossref]
  • [19] J. W. Wang, Q. H. Ma, L. Zeng, M. S. Abd-Elouahab, Chaos 21, 013121 (2011) http://dx.doi.org/10.1063/1.3555836[Crossref]
  • [20] H. Delavari, D. M. Senejohnny, D. Baleanu, Cent. Eur. J. Phys. 10, 1095 (2012) http://dx.doi.org/10.2478/s11534-012-0073-4[Crossref]
  • [21] I. Leyva et al., Phys. Rev. Lett. 108, 168702 (2012) http://dx.doi.org/10.1103/PhysRevLett.108.168702[Crossref]
  • [22] M. Ciszak, S. Euzzor, A. Geltrude, F. T. Arecchi, R. Meucci, Commun. Nonlinear Sci. Numer. Simulat. 18, 938 (2013). http://dx.doi.org/10.1016/j.cnsns.2012.08.038[Crossref]
  • [23] I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999)
  • [24] J. Klafter, S. C. Lim, R. Metzler, Eds., Fractional Dynamics: Recent Advances (World Scientific, Singapore, 2011)
  • [25] K. P. Wilkie, C. S. Drapaca, S. Sivaloganathan, Appl. Math. Comput. 217, 8693 (2011) http://dx.doi.org/10.1016/j.amc.2011.03.115[Crossref]
  • [26] K. Wei, S. Gao, S. Zhong, H. Ma, PLoS ONE 7, e38383 (2012) http://dx.doi.org/10.1371/journal.pone.0038383[Crossref]
  • [27] T. S. Zhou, C. P. Li, Physica D 212, 111 (2005) http://dx.doi.org/10.1016/j.physd.2005.09.012[Crossref]
  • [28] J. Wang, Y. Zhang, Phys. Lett. A 374, 1464 (2010) http://dx.doi.org/10.1016/j.physleta.2010.01.042[Crossref]
  • [29] S. S. Delshad, M. M. Asheghan, M. H. Beheshti, Commun. Nonlinear Sci. Numer. Simul. 16, 3815 (2011) http://dx.doi.org/10.1016/j.cnsns.2010.12.035[Crossref]
  • [30] Y. Cao, Y. Li, W. Ren, Y. Q. Chen, IEEE Trans. Syst., Man, Cybern. B, Cybern. 40, 362 (2010) http://dx.doi.org/10.1109/TSMCB.2009.2024647[Crossref]
  • [31] J. Wang, X. Xiong, Chaos 22, 023102 (2012) http://dx.doi.org/10.1063/1.3701726[Crossref]
  • [32] X. J. Wu, H. T. Lu, Chin. Phys. B 19, 070511 (2010) http://dx.doi.org/10.1088/1674-1056/19/7/070511[Crossref]
  • [33] M. M. Asheghan, J. Míguez, M. T. Hamidi-Beheshti, M. S. Tavazoei, Chaos 21, 033121 (2011) http://dx.doi.org/10.1063/1.3629986[Crossref]
  • [34] L. Chen, Y. Chai, R. Wu, J. Sun, T. Ma, Phys. Lett. A 376, 2381 (2012) http://dx.doi.org/10.1016/j.physleta.2012.05.060[Crossref]
  • [35] T. T. Hartley, C. F. Lorenzo, H. K. Qammer, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 42, 485 (1995) http://dx.doi.org/10.1109/81.404062[Crossref]
  • [36] J. G. Lu, Chaos Solitons Fract. 27, 1125 (2005) http://dx.doi.org/10.1016/j.chaos.2005.02.023[Crossref]
  • [37] W. M. Ahmad, W. M. Harb, Chaos Solitons Fract. 18, 693 (2003) http://dx.doi.org/10.1016/S0960-0779(02)00644-6[Crossref]
  • [38] C. G. Li, G. Chen, Physica A 341, 55 (2004) http://dx.doi.org/10.1016/j.physa.2004.04.113[Crossref]
  • [39] G. H. Erjaee, M. Alnasr, Discrete Dyn. Nat. Soc. 2009, 753746 (2009) http://dx.doi.org/10.1155/2009/753746[Crossref]
  • [40] H. Deng, T. Li, Q. Wang, H. Li, Chaos Solitons Fract. 41, 962 (2009) http://dx.doi.org/10.1016/j.chaos.2008.04.034[Crossref]
  • [41] C. K. Ahn, Nonlinear Anal.: Hybrid Syst. 9, 1 (2013) http://dx.doi.org/10.1016/j.nahs.2013.01.002[Crossref]
  • [42] C. K. Ahn, S. T. Jung, S. K. Kang, S. C. Joo, Commun. Nonlinear Sci. Numer. Simulat. 15, 2168 (2010) http://dx.doi.org/10.1016/j.cnsns.2009.08.009[Crossref]
  • [43] C. K. Ahn, Prog. Theor. Phys 123, 421 (2010) http://dx.doi.org/10.1143/PTP.123.421[Crossref]
  • [44] C. K. Ahn, Nonlinear Dyn. 60, 295 (2010) http://dx.doi.org/10.1007/s11071-009-9596-7[Crossref]
  • [45] C. K. Ahn, Phys. Lett. A 373, 1729 (2009) http://dx.doi.org/10.1016/j.physleta.2009.03.032[Crossref]
  • [46] A. J. Laub, Matrix Analysis for Scientists and Engineers (SIAM, Philadelphia, 2005) http://dx.doi.org/10.1137/1.9780898717907[Crossref]
  • [47] M. Chilali, P. Gahinet, P. Apkarian, IEEE Trans. Autom. Control 44, 2257 (1999) http://dx.doi.org/10.1109/9.811208[Crossref]
  • [48] P. P. Khargonekar, I. R. Petersen, K. Zhou, IEEE Trans. Autom. Control 35, 356 (1990) http://dx.doi.org/10.1109/9.50357[Crossref]
  • [49] D. Matignon, Stability results for fractional differential equations with applications to control processing, in Proceedings of the IMACS-IEEE CESA (Lille, France, 1996), pp. 963–968
  • [50] S. Boyd, L. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (SIAM, Philadelphia, 1994) http://dx.doi.org/10.1137/1.9781611970777[Crossref]
  • [51] C. Li, Z. Zhao, J. Shanghai Univ. (Engl. Ed). 13, 197 (2009) http://dx.doi.org/10.1007/s11741-009-0302-1[Crossref]
  • [52] D. L. Qian, C. P. Li, R. P. Agarwal, P. J. Y. Wong, Math. Comput. Model. 52, 862 (2010) http://dx.doi.org/10.1016/j.mcm.2010.05.016[Crossref]
  • [53] C. P. Li, F. R. Zhang, Eur. Phys. J. Spec. Top. 193, 27 (2011) http://dx.doi.org/10.1140/epjst/e2011-01379-1[Crossref]
  • [54] Y. Li, Y. Q. Chen, I. Podlubny, Automatica 45, 1965 (2009) http://dx.doi.org/10.1016/j.automatica.2009.04.003[Crossref]
  • [55] X. J. Wen, Z. M. Wu, J. G. Lu, IEEE Trans. Circuits Syst. II, Exp. Briefs 55, 1178 (2008) http://dx.doi.org/10.1109/TCSII.2008.2002571[Crossref]
  • [56] L. Chen, Y. Chai, R. Wu, J. Yang, IEEE Trans. Circuits Syst. II, Exp. Briefs 59, 602 (2012) http://dx.doi.org/10.1109/TCSII.2012.2206936[Crossref]
  • [57] C. P. Li, Y. T. Ma, Nonlinear Dyn. 71, 621 (2013) http://dx.doi.org/10.1007/s11071-012-0601-1[Crossref]
  • [58] K. Diethelm, N. J. Ford, A. D. Freed, Nonlinear Dyn. 29, 3 (2002) http://dx.doi.org/10.1023/A:1016592219341[Crossref]

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-013-0228-y
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.