Parametric study of the fractional-order Chen-Lee system

Chaos, Solitons and Fractals

Volumn 37, Issue 3, 2008, Pages 817-826

  Tam, Lap Mou ^a   Si Tou, Wai Meng ^a  

^a UNIVERSITY OF MACAU   (Macao)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC SYSTEMS; LYAPUNOV FUNCTIONS; NUMERICAL METHODS; PARAMETER ESTIMATION;

CHEN-LEE SYSTEM; DYNAMIC BEHAVIORS; FRACTIONAL-ORDER SYSTEMS;

SYSTEMS ANALYSIS;

EID: 40249084124     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.09.067     Document Type: Article

References (42)

1. I. Podlubny Fractional differential equations 1999 Academic Press New York
2. R. Hilfer Applications of fractional calculus in physics 2001 World Scientific New Jersey
3. R.L. Bagley R.A. Calico Fractional order state equations for the control of viscoelastically damped structures J Guid Control Dyn 14 1991 304 311
4. R.C. Koeller Application of fractional calculus to the theory of viscoelasticity J Appl Mech 51 1984 199
5. H.H. Sun A.A. Abdelwahed B. Onaral Linear approximation for transfer function with a pole of fractional order IEEE Trans Autom Control 29 1984 441 444
6. M. Ichise Y. Nagayanagi T. Kojima An analog simulation of noninteger order transfer functions for analysis of electrode process J Electroanal Chem 33 1971 253 265
7. O. Heaviside Electromagnetic theory 1971 Chelsea New York
8. N. Laskin Fractional market dynamics Physica A 287 2000 482 492
9. D. Kunsezov A. Bulagc G.D. Dang Quantum levy processes and fractional kinetics Phys Rev Lett 82 1999 1136 1139
10. A. Oustaloup J. Sabatier P. Lanusse From fractal robustness to CRONE control Fract Calculus Appl Anal 2 1999 1 30
11. A. Oustaloup F. Levron F. Nanot B. Mathieu Frequency band complex non integer differentiator: characterization and synthesis IEEE Trans CAS-I 47 2000 25 40
12. T.Q. Chen K. Moore Discretization schemes for fractional-order differentiators and integrators IEEE Trans CAS-I 79 2002 363 367
13. T.T. Hartley C.F. Lorenzo Dynamics and control of initialized fractional-order systems Nonlinear Dyn 29 2002 201 233
14. C. Hwang J.F. Leu S.Y. Tsay A note on time-domain simulation of feedback fraction-order systems IEEE Trans Autom Control 47 2002 625 631
15. I. Podlubny I. Petras B.M. Vinagre P. O’Leary L. Dorcak Analogue realizations of fractional-order controllers Nonlinear Dyn 29 2002 281 286
16. G.M. Zaslavsky Chaos, fractional kinetics, and anomalous transport Phys Rep 371 2002 461 580
17. T.T. Hartley C.F. Lorenzo H.K. Qammer Chaos in a fractional order Chua’s system IEEE Trans CAS-I 42 1995 485 490
18. Arena P, Caponetto R, Fortuna L, Porto D. Chaos in a fractional order duffing system. In: Proceedings of ECCTD, Budapest; 1997. p. 1259–62.
19. W. Ahmad R. El-Khazali A. El-Wakli Fractional-order Wien-bridge oscillator Electron Lett 37 2001 1110 1112
20. W.M. Ahmad J.C. Sprott Chaos in fractional-order autonomous nonlinear systems Chaos, Solitons & Fractals 16 2003 339 351
21. W.M. Ahmad W.M. Harb On nonlinear control design for autonomous chaotic systems of integer and fractional orders Chaos, Solitons & Fractals 18 2003 693 701
22. I. Grigorenko E. Grigirenko Chaotic dynamics of the fractional Lorenz system Phys Rev Lett 91 2003 034101
23. P. Arena R. Caponetto L. Fortuna D. Porto Bifurcation and chaos in noninteger order cellular neural networks Int J Bifurcat Chaos 7 1998 1527 1539
24. P. Arena L. Fortuna D. Porto Chaotic behavior in noninteger-order cellular neural networks Phys Rev E 61 2000 776 781
25. Z.M. Ge C.X. Yi Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order system Chaos, Solitons & Fractals 32 2007 42 61
26. C. Li G. Chen Chaos and hyperchaos in fractional order Rössler equation Physica A 341 2004 55 61
27. L.J. Sheu H.K. Chen J.H. Chen L.M. Tam Chaotic dynamics of the fractionally damped Duffing equation Chaos, Solitons & Fractals 32 2007 1459 1468
28. H.K. Chen C.I. Lee Anti-control of chaos in rigid body motion Chaos, Solitons & Fractals 21 2004 957 965
29. H.K. Chen Global chaos synchronization of new chaotic systems via nonlinear control Chaos, Solitons & Fractals 23 2005 1245 1251
30. H.K. Chen Synchronization of two different chaotic systems: a new system and each of the dynamical systems Lorenz, Chen and Lü Chaos, Solitons & Fractals 25 2005 1049 1056
31. L.J. Sheu H.K. Chen J.H. Chen L.M. Tam Chaos in a new system with fractional order Chaos, Solitons & Fractals 31 2007 1203 1212
32. Z.M. Ge J.W. Cheng Y.S. Chen Chaos anticontrol and synchronization of three time scales brushless DC motor system Chaos, Solitons & Fractals 22 2004 1165 1182
33. Z.M. Ge C.I. Lee Control, anticontrol and synchronization of chaos for an autonomous rotational machine system with time-delay Chaos, Solitons & Fractals 23 2005 1855 1864
34. M. Perc M. Marhl Chaos in temporarily destabilized regular systems with the slow passage effect Chaos, Solitons & Fractals 27 2006 395 403
35. J.H. Park Chaos synchronization between two different chaotic dynamical systems Chaos, Solitons & Fractals 27 2006 549 554
36. M. Marhl M. Perc Determining the flexibility of regular and chaotic attractors Chaos, Solitons & Fractals 28 2006 822 833
37. M. Caputo Linear models of dissipation whose Q is almost frequency independent—II Geophys J R Astron Soc 13 1967 529 539
38. K. Diethelm An algorithm for the numerical solution of differential equations of fractional order Electron Trans Numer Anal 5 1997 1 6
39. K. Diethelm N.J. Ford A.D. Freed A predictor–corrector approach for the numerical solution of fractional differential equations Nonlinear Dyn 29 2002 3 22
40. A. Wolf J.B. Swinney H.L. Swinney J.A. Vastano Determining Lyapunov exponents from a time series Physica D 16 1985 285 317
41. S. Sato M. Sano Y. Sawada Practical methods of measuring the generalized dimension and the largest Lyapunov exponent in high dimensional chaotic system Prog Theor Phys 77 1987 1 5
42. M.T. Rosenstein J.J. Collins C.J. De Luca A practical method for calculating largest Lyapunov exponents from small data sets Physica D 65 1993 117 134