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HomeKey Engineering MaterialsKey Engineering Materials Vols. 474-476Chaotic Control in a Fractional-Order Modified Van...

Chaotic Control in a Fractional-Order Modified Van Der Pol Oscillator

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Abstract:

The dynamics of fractional-order systems have attracted increasing attention in recent years. In this paper, we study the chaotic behaviors in a fractional-order modified van der Pol oscillator. We find that chaos exists in the fractional-order modified van der Pol oscillator with order less than 3. In addition, the lowest order we find for chaos to exist in such system is 2.4. Finally, a simple, but effective, linear feedback controller is also designed to stabilize the fractional order chaotic van der Pol oscillator.

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Advanced Materials and Computer Science

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Periodical:

Key Engineering Materials (Volumes 474-476)

Pages:

83-88

DOI:

https://doi.org/10.4028/www.scientific.net/KEM.474-476.83

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Online since:

April 2011

Authors:

Xin Gao

Keywords:

Chaos, Chaotic Control, Fractional Order, Van Der Pol Oscillator

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© 2011 Trans Tech Publications Ltd. All Rights Reserved

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[1] R.C. Koeller：J. Appl. Mech., Vol. 51(1984), p.299.

[2] M. Ichise, Y. Nagayanagi and T. Kojima：J. Electroanal. Chem., Vol. 33(1971), p.253.

[3] B. Mandelbrot：IEEE Trans. Inform Theory, 1967, IT-13.

[4] O. Heaviside：Electromagnetic theory. New York: Chelsea, (1971).

[5] T.T. Hartly, C.F. Lorenzo and H.K. Qammer：IEEE Trans. CAS-I: Fundamental Theory and Applications, Vol. 42(1995), p.485.

[6] W. Ahmad, R. EI-khazali and A.S. EIwakil: Electron. Lett., Vol. 37(2001), p.1110.

[7] P. Arena，R. Caponetto，L. Fortuna and D. Porto: Proceeding of the ECCTD, Budapest, 1997, p.1259.

[8] W.M. Ahmad and J.C. Sprott：Chaos, Solitons & Fractals. Vol. 16(2003), p.339.

[9] E.J. Doedel, E. Freire，E. Gamero and A.J. Rodriguez：Journal of Sound and Vibration, Vol. 256(2002), p.755.

[10] J. Guckenheimer and P. Holmes：Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag, (1983).

[11] I. Podlubny：Fractional differential equations. New York: Academic Press, (1999).

[12] W.M. Ahmad and A.M. Harb：Chaos, Solitons & Fractals. Vol. 18(2003), p.693.

[13] C. Li, X. Liao and J. Yu: Phys Rev E. Vol. 68 (2003), 067203.

[14] E. Ott, C. Grebogi and J.A. Yorke: Phys Rev Lett., Vol. 64(1990), p.1196.