Chaos in Chen's system with a fractional order

Chaos, Solitons and Fractals

Volumn 22, Issue 2, 2004, Pages 443-450

  Li, Changpin ^a,b   Peng, Guojun ^a  

^a SHANGHAI UNIVERSITY   (China)

^b UNIVERSITY OF PRETORIA   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DIFFERENTIAL EQUATIONS; FREQUENCY DOMAIN ANALYSIS; INTEGRAL EQUATIONS; LYAPUNOV METHODS; MATHEMATICAL OPERATORS; PHASE DIAGRAMS;

FRACTIONAL ORDER; INTEGRAL OPERATORS;

CHAOS THEORY;

EID: 1842832060     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2004.02.013     Document Type: Article

References (15)

1. Butzer P.L., Westphal U. An introduction to fractional calculus. Hilfer R. Applications of fractional calculus in physics. 2000;1-85 World Scientific, Singapore.
2. Podlubny I. Fractional differential equations. 1999;Academic Press, San Diego.
3. Samko S.G., Kilbas A.A., Marichev O.I. Fractional integrals and derivatives: theory and applications. 1993;Gordan and Breach, Amsterdam.
4. Caputo M. Linear models of dissipation whose. Q is almost frequency independent, II Geophys. J. R. Astron. Soc. 13:1967;529-539.
5. Chen G., Ueta T. Yet another chaotic attractor. Int. J. Bifurc. Chaos. 9:1999;1465-1466.
6. Diethelm K. An algorithm for the numerical solution of differential equations of fractional order. Elec. Trans. Numer. Anal. 5:1997;1-6.
7. Diethelm K., Ford N.J. Analysis of fractional differential equations. J. Math. Anal. Appl. 265:2002;229-248.
8. Diethelm K., Ford N.J., Freed A.D. A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn. 29:2002;3-22.
9. Diethelm K., Freed A.D. The FracPECE subroutine for the numerical solution of differential equations of fractional order. Heinzel S., Plesser T. Forschung und wissenschaftliches Rechnen. 1999;57-71 Gesellschaft für wissenschaftliche Datenverarbeitung, Göttingen.
10. Wolf A., Swinney J.B., Swinney H.L., Vastano J.A. Determining Lyapunov exponents from a time series. Phys. D. 16:1985;285-317.
11. Sato S., Sano M., Sawada Y. Practical methods of measuring the generalized dimension and the largest Lyapunov exponent in high dimensional chaotic system. Prog. Theor. Phys. 77:1987;1-5.
12. Rosenstein M.T., Collins J.J., De Luca C.J. A practical method for calculating largest Lyapunov exponents from small data sets. Phys. D. 65:1993;117-134.
13. Rosenstein M.T., Collins J.J., De Luca C.J. Reconstruction expansion as a geometry-based framework for choosing delay times. Phys. D. 73:1994;82-98.
14. Charef A., Sun H.H., Tsao Y.Y., Onaral B. Fractional systems as represented by singularity function. IEEE Trans. Auto Control. 37(9):1993;1465-1470.
15. Hartley T.T., Lorenzo, Qammer H.K. Chaos in a fractional order Chua's system. IEEE Trans. CAS I. 42(8):1995;485-490.