Synchronizing Fractional Chaotic Genesio-Tesi System via Backstepping Approach

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Abstract. Based on fractional nonlinear stable theorem, backstepping approach for designing controller is extended to fractional order chaotic system. The controller is designed to synchronize fractional order Newton-Leipnik chaotic system via the backstepping approach. Numerical simulation certifies effectiveness of the approach.

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1244-1248

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November 2012

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© 2012 Trans Tech Publications Ltd. All Rights Reserved

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[1] P.L. Butzer, U. Westphal, An introduction to fractional calculus. World Scientific, Singapore, 2000.

Google Scholar

[2] J. Sabatier, S. Poullain etc., Robust speed control of a low damped electromechanical system based on CRONE control: application to a four mass experimental test bench, Nonlinear Dyn. 38(2004) 383-400.

DOI: 10.1007/s11071-004-3768-2

Google Scholar

[3] M. Caputo, F, Mainardi, A new dissipation model based on memory mechanism, Pure Appl Geophys. 91(1971) 134-47.

DOI: 10.1007/bf00879562

Google Scholar

[4] F. Mainardi, Y. Luchko, G. Pagnini, The fundamental solution of the space-time fractional diffusion equation, Fractional Calculus Appl Anal 4(2001)153-92.

Google Scholar

[5] O.P. Agrawal, Solution for a fractional diffusion-wave equation defined in a bounded domain, Nonlinear Dyn. 29 (2002) 145-55.

Google Scholar

[6] T.J. Anastasio, The fractional-order dynamics of brainstem vestibulo-oculomotor neurons, Biol Cybern. 72(1994) 69-79.

DOI: 10.1007/bf00206239

Google Scholar

[7] M.D. Ortigueira, J.A.T. Machado, Fractional calculus applications in signals and systems, Signal Process 86(2006) 2503-4.

DOI: 10.1016/j.sigpro.2006.02.001

Google Scholar

[8] C.G. Li, G. Chen, Chaos and hyperchaos in the fractional-order R¨ ossler equations, Physica A 341 (2004) 55-61.

Google Scholar

[9] C.G. Li, X. Liao, J. Yu, Synchronization of fractional order chaotic systems, Phys. Rev. E 68 (2003) 067203.

Google Scholar

[10] T.S. Zhou, C.P. Li, Synchronization in fractional-order differential systems, Physica D 212 (2005) 111-125.

Google Scholar

[11] J.G. Lu, Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal, Chaos Solitons Fractals 27 (2006) 519-525.

DOI: 10.1016/j.chaos.2005.04.032

Google Scholar

[12] J.B. Hu, Y. Han, L.D. Zhao, A novel stable theorem for fractional system and applying it in synchronizing fractional chaotic system based on backstepping approach, Acta Phys. Sin. 58 (2009) 2235-2239.

DOI: 10.7498/aps.58.2235

Google Scholar

[13] M. Caputo, Linear models of dissipation whose Q is almost frequency independent, Part II, J. Roy. Austral. Soc. 13(1967)529-539.

DOI: 10.1111/j.1365-246x.1967.tb02303.x

Google Scholar

[14] M.R. Faieghi, H. Delavari, Chaos in fractional-order Genesio-Tesi system and its synchronization. Commun Nonlinear Sci Numer Simulat, 17(2012) 731-741.

DOI: 10.1016/j.cnsns.2011.05.038

Google Scholar

[15] W.H. Deng, Smoothness and stability of the solutions for nonlinear fractional differential equations, Nonlinear Anal., Real World Appl. 72(2009) 1768–1777.

DOI: 10.1016/j.na.2009.09.018

Google Scholar