Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-17T08:21:31.016Z Has data issue: false hasContentIssue false
  • English
  • Français

PINNING SYNCHRONIZATION OF FRACTIONAL-ORDER COMPLEX NETWORKS BY A SINGLE CONTROLLER

Part of: Control systems

Published online by Cambridge University Press:  13 March 2017

Q. FANG Open the ORCID record for Q. FANG [Opens in a new window]  and
J. PENG
Q. FANG*
Affiliation:
Department of Applied Mathematics, Xi’an Jiaotong University, Xi’an 710049, China College of Sciences, China Jiliang University, Hangzhou 310018, China email [email protected], [email protected]
J. PENG
Affiliation:
Department of Applied Mathematics, Xi’an Jiaotong University, Xi’an 710049, China College of Sciences, China Jiliang University, Hangzhou 310018, China email [email protected], [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate the state feedback pinning synchronization of fractional-order complex networks. Based on the stability theory of fractional-order differential systems and state feedback control by a single controller, synchronization conditions for fractional-order complex networks are given. We assume that the coupling matrix is irreducible, and provide a numerical example to illustrate the validity of the proposed conclusions.

Keywords

fractional-order complex networkssynchronizationlinearly coupled networksstate feedback

MSC classification

Primary: 93C15: Systems governed by ordinary differential equations
Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 3-4 , April 2017 , pp. 324 - 332
Copyright
© 2017 Australian Mathematical Society 

References

Chai, Y., Chen, L., Wu, R. and Sun, J., “Adaptive pinning synchronization in fractional-order complex dynamical networks”, Phys. A 391 (2012) 5746–5758; doi:10.1016/j.physa.2012.06.050.CrossRefGoogle Scholar
Chen, L., Chai, Y. and Wu, R., “Lag projective synchronization in fractional-order chaotic (hyperchaotic) systems”, Phys. Lett. A 375(21) (2011) 2099–2110;doi:10.1016/j.physleta.2011.04.015.CrossRefGoogle Scholar
Chen, T., Liu, X. and Lu, W., “Pinning complex networks by a single controller”, IEEE Trans. Circuits Syst. I 54(6) (2007) 1317–1326; doi:10.1109/TCSI.2007.895383.CrossRefGoogle Scholar
Chen, H., Sheu, G., Lin, Y. and Chen, C., “Chaos synchronization between two different chaotic systems via nonlinear feedback control”, Nonlinear Anal. 70(21) (2009) 4393–4401;doi:10.1016/j.na.2008.10.069.CrossRefGoogle Scholar
Emelianova, Y. P., Emelyanov, V. V. and Ryskin, N. M., “Synchronization of two coupled multimode oscillators with time-delayed feedback”, Commun. Nonlinear Sci. Numer. Simul. 19(10) (2014) 3778–3791; doi:10.1016/j.cnsns.2014.03.031.CrossRefGoogle Scholar
Grigorenko, I. and Grigorenko, E., “Chaotic dynamics of the fractional Lorenz system”, Phys. Rev. Lett. 91 (2003) 034101; doi:10.1103/PhysRevLett.91.034101.CrossRefGoogle ScholarPubMed
Hartley, T. T., Lorenzo, C. F. and Qammer, H. K., “Chaos on a fractional Chua’s system”, IEEE Trans. Circuits Syst. I 42(8) (1995) 485–790; doi:10.1109/81.404062.CrossRefGoogle Scholar
Ho, M. and Hung, Y., “Synchronization of two different systems by using generalized active control”, Phys. Lett. A 301(5-6) (2002) 424–428; doi:10.1016/S0375-9601(02)00987-8.CrossRefGoogle Scholar
Hu, J., Han, Y. and Zhao, L., “A novel stablility theorem for fractional systems and its applying in synchronizing fractional chaotic system based on back-stepping approach”, Acta Phys. Sinica 58(4) (2009) 2235–2239 (in Chinese); http://wulixb.iphy.ac.cn/CN/Y2009/V58/I4/2235.Google Scholar
Li, C. and Chen, G., “Chaos and hyperchaos in the fractional-order Rössler equations”, Phys. A 341 (2004) 55–61; doi:10.1016/j.physa.2004.04.113.CrossRefGoogle Scholar
Li, C. and Chen, G., “Chaos in the fractional order Chen system and its control”, Chaos Solitons Fractals 22 (2005) 549–554; doi:10.1016/j.chaos.2004.02.035.CrossRefGoogle Scholar
Lu, J., “Chaotic dynamics of the fractional-order Lü system and its synchronization”, Phys. Lett. A 354 (2006) 305–311; doi:10.1016/j.physleta.2006.01.068.CrossRefGoogle Scholar
Lu, W. and Chen, T., “Synchronization of coupled connected neural networks with delays”, IEEE Trans. Circuits Syst. I 51(12) (2004) 2491–2503; doi:10.1109/TCSI.2004.838308.CrossRefGoogle Scholar
Lu, W. and Chen, T., “New approach to synchronization analysis of linearly coupled ordinary differential systems”, Phys. D 213 (2006) 214–230; doi:10.1016/j.physd.2005.11.009.CrossRefGoogle Scholar
Lu, J. and Chen, G., “Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control: An LMI approach”, Chaos Solitons Fractals 41 (2009) 2293–2300; doi:10.1016/j.chaos.2008.09.024.CrossRefGoogle Scholar
Néda, Z., Ravasz, E., Brechet, Y., Vicsek, T. and Barabási, A. L., “The sound of many hands clapping”, Nature 403 (2000) 849–850; doi:10.1038/35002660.CrossRefGoogle ScholarPubMed
Park, J. H. and Kwon, O. M., “A novel criterion for delayed feedback control of time-delay chaotic systems”, Chaos Soliton Fractals 23 (2005) 495–501; doi:10.1016/j.chaos.2004.05.023.CrossRefGoogle Scholar
Podlubny, I., Fractional differential equations (Academic Press, San Diego, 1999);http://store.elsevier.com/product.jsp?isbn=9780125588409.Google Scholar
Radawan, A. G., Moaddy, K., Salama, K. N., Momani, S. and Hashim, I., “Control and switching synchronization of fractional order chaotic systems using active control technique”, J. Adv. Res. 5(1) (2014) 125–132; doi:10.1016/j.jare.2013.01.003.CrossRefGoogle Scholar
Tang, Y., Wang, Z. and Fang, J., “Pinning control of fractional-order weighted complex networks”, Chaos 19 (2009) 013112; doi:10.1063/1.3068350.CrossRefGoogle ScholarPubMed
Wang, Y. and Li, T., “Synchronization of fractional order complex dynamical networks”, Phys. A 428 (2015) 1–12; doi:10.1016/j.physa.2015.02.051.CrossRefGoogle Scholar
Zaid, O., “A note on phase synchronization in coupled chaotic fractional order systems”, Nonlinear Anal. 13(2) (2012) 779–789; doi:10.1016/j.nonrwa.2011.08.016.Google Scholar