Chaos synchronization of fractional order modified duffing systems with parameters excited by a chaotic signal

Chaos, Solitons and Fractals

Volumn 35, Issue 4, 2008, Pages 705-717

  Ge, Zheng Ming ^a   Ou, Chan Yi ^a  

^a NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS; FUNCTION EVALUATION; NUMERICAL METHODS; PARAMETER ESTIMATION; SYNCHRONIZATION;

CHAOS SYNCHRONIZATIONS; CHAOTIC SIGNAL; CHAOTIC STATE VARIABLES; DUFFING SYSTEMS;

CHAOTIC SYSTEMS;

EID: 34748813039     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.05.101     Document Type: Article

References (62)

1. Pecora L.M., and Carroll T.L. Synchronization in chaotic systems. Phys Rev Lett 64 (1990) 821-824
2. Carroll T.L., Heagy J.F., and Pecora L.M. Transforming signals with chaotic synchronization. Phys Rev E 54 (1996) 4676-4680
3. Kocarev L., and Parlitz U. Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. Phys Rev Lett 76 (1996) 1816-1819
4. Rosenblum M.G., Pikovsky A.S., and Kurths J. Phase synchronization of chaotic oscillators. Phys Rev Lett 76 (1996) 1804-1807
5. Yang S.S., and Duan C.K. Generalized synchronization in chaotic systems. Chaos, Solitons & Fractals 9 (1998) 1703-1707
6. Chen G., and Liu S.T. On generalized synchronization of spatial chaos. Chaos, Solitons & Fractals 15 (2003) 311-318
7. Kim C.M., Rim S., Kye W.H., Ryu J.W., and Park Y.J. Anti-synchronization of chaotic oscillators. Phys Lett A 320 (2003) 39-46
8. Yang S.P., Niu H.Y., Tian G., et al. Synchronizing chaos by driving parameter. Acta Phys Sin 50 (2001) 619-623
9. Dai D., and Ma XK. Chaos synchronization by using intermittent parametric adaptive control method. Phys Lett A 288 (2001) 23-28
10. Chen H.K. 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
11. Chen H.K., and Lin T.N. Synchronization of chaotic symmetric gyros by one-way coupling conditions. ImechE Part C: J Mech Eng Sci 217 (2003) 331-340
12. Chen H.K. Chaos and chaos synchronization of a symmetric gyro with linear-plus-cubic damping. J Sound Vib 255 (2002) 719-740
13. Ge Z.M., Yu T.C., and Chen Y.S. Chaos synchronization of a horizontal platform system. J Sound Vib (2003) 731-749
14. Ge Z.M., and Lin T.N. Chaos, chaos control and synchronization of electro-mechanical gyrostat system. J Sound Vib 259 3 (2003)
15. Ge Z.M., and Chen Y.S. Synchronization of unidirectional coupled chaotic systems via partial stability. Chaos, Solitons & Fractals 21 (2004) 101-111
16. Ge Z.M., and Chen C.C. Phase synchronization of coupled chaotic multiple time scales systems. Chaos, Solitons & Fractals 20 (2004) 639-647
17. Ge Z.M., Lin C.C., and Chen Y.S. Chaos, chaos control and synchronization of vibrometer system. J Mech Eng Sci 218 (2004) 1001-1020
18. Chen H.K., Lin T.N., and Chen J.H. The stability of chaos synchronization of the Japanese attractors and its application. Jpn J Appl Phys 42 12 (2003) 7603-7610
19. Ge Z.M., and Shiue J.S. Non-linear dynamics and control of chaos for Tachometer. J Sound Vib 253 4 (2002)
20. Ge Z.M., and Lee C.I. Non-linear dynamics and control of chaos for a rotational machine with a hexagonal centrifugal governor with a spring. J Sound Vib 262 (2003) 845-864
21. Ge Z.M., Hsiao C.M., and Chen Y.S. Non-linear dynamics and chaos control for a time delay Duffing system. Int J Nonlinear Sci Numer 6 2 (2005) 187-199
22. Ge Z.M., Tzen P.C., and Lee S.C. Parametric analysis and fractal-like basins of attraction by modified interpolates cell mapping. J Sound Vib 253 3 (2002)
23. Ge Z.M., and Lee S.C. Parameter used and accuracies obtain in MICM global analyses. J Sound Vib 272 (2004) 1079-1085
24. Ge Z.M., and Leu W.Y. Chaos synchronization and parameter identification for loudspeaker system. Chaos, Solitons & Fractals 21 (2004) 1231-1247
25. Ge Z.M., and Chang C.M. Chaos synchronization and parameter identification for single time scale brushless DC motor. Chaos, Solitons & Fractals 20 (2004) 889-903
26. Ge Z.M., and Lee J.K. Chaos synchronization and parameter identification for gyroscope system. Appl Math Comput 63 (2004) 667-682
27. Ge Z.M., and Cheng J.W. Chaos synchronization and parameter identification of three time scales brushless DC motor. Chaos, Solitons & Fractals 24 (2005) 597-616
28. Ge Z.M., and Chen Y.S. Adaptive synchronization of unidirectional and mutual coupled chaotic systems. Chaos, Solitons & Fractals 26 (2005) 881-888
29. Chen H.K. Global chaos synchronization of new chaotic systems via nonlinear control. Chaos, Solitons & Fractals 4 (2005) 1245-1251
30. Chen H.K., and Lee C.I. Anti-control of chaos in rigid body motion. Chaos, Solitons & Fractals 21 (2004) 957-965
31. Ge Z.M., and Wu H.W. Chaos synchronization and chaos anticontrol of a suspended track with moving loads. J Sound Vib 270 (2004) 685-712
32. Ge Z.M., Yu C.Y., and Chen Y.S. Chaos synchronization and chaos anticontrol of a rotational supported simple pendulum. JSME Int J, Ser C 47 1 (2004) 233-241
33. Ge Z.M., and Leu W.Y. Anti-control of chaos of two-degree-of-freedom louder speaker system and chaos system of different order system. Chaos, Solitons & Fractals 20 (2004) 503-521
34. Ge Z.M., Cheng J.W., and Chen Y.S. Chaos anticontrol and synchronization of three time scales brushless DC motor system. Chaos, Solitons & Fractals 22 (2004) 1165-1182
35. Ge Z.M., and Lee C.I. Anticontrol and synchronization of chaos for an autonomous rotational machine system with a hexagonal centrifugal governor. Chaos, Solitons & Fractals 282 (2005) 635-648
36. Ge Z.M., and Lee C.I. Control, anticontrol and synchronization of chaos for an autonomous rotational machine system with time-delay. Chaos, Solitons & Fractals 23 (2005) 1855-1864
37. He G.L., and Zhou S.P. What is the exact condition for fractional integrals and derivatives of Besicovitch functions to have exact box dimension?. Chaos, Solitons & Fractals 26 (2005) 867-879
38. Yao K., Su W.Y., and Zhou S.P. On the connection between the order of fractional calculus and the dimensions of a fractal function. Chaos, Solitons & Fractals 23 (2005) 621-629
39. Guy J. Fractional master equation: Non-standard analysis and Liouville-Riemann derivative. Chaos, Solitons & Fractals 12 (2001) 2577-2587
40. Elwakil S.A., and Zahran M.A. Fractional integral representation of master equation. Chaos, Solitons & Fractals 10 (1999) 1545-1548
41. Sun H.H., Abdelwahad A.A., and Onaral B. IEEE Trans Autom Control 29 (1984) 441
42. Ichise M., Nagayanagi Y., and Kojima T. J Electroanal Chem 33 (1971) 253
43. Heaviside O. Electromagnetic Theory (1971), Chelsea, New York
44. Oustaloup A., Levron F., Nanot F., and Mathieu B. Frequency band complex non integer differentiator: Characterization and synthesis. IEEE Trans CAS-I 47 (2000) 25-40
45. Chen Y.Q., and Moore K. Discretization schemes for fractional-order differentiators and integrators. IEEE Trans CAS-I 49 (2002) 363-367
46. Hartley T.T., and Lorenzo C.F. Dynamics and control of initialized fractional-order systems. Nonlinear Dyn 29 (2002) 2002-2033
47. Hwang C., Leu J.F., and Tsay S.Y. A note on time-domain simulation of feedback fractional-order systems. IEEE Trans Auto Control 47 (2002) 625-631
48. Podlubny I., Petras I., Vinagre B.M., OLeary P., and Dorcak L. Analogue realizations of fractional-order controllers. Nonlinear Dyn 29 (2002) 281-296
49. Hartley T.T., Lorenzo C.F., and Qammer H.K. Chaos in a fractional order Chua's system. IEEE Trans CAS-I 42 (1995) 485-490
50. Arena P, Caponetto R, Fortuna L, Porto D. Chaos in a fractional order Duffing system. In: Proc ECCTD, Budapest, 1997, pp. 1259-62.
51. Ahmad W.M., and Sprott J.C. Chaos in fractional-order autonomous nonlinear systems. Chaos, Solitons & Fractals 16 (2003) 339-351
52. Ahmad W.M., and Harb W.M. On nonlinear control design for autonomous chaotic systems of integer and fractional orders. Chaos, Solitons & Fractals 18 (2003) 693-701
53. Ahmad W., El-Khazali R., and El-Wakil A. Fractional-order Wien-bridge oscillator. Electron Lett 37 (2001) 1110-1112
54. Grigorenko L., and Grigorenko E. Chaotic dynamics of the fractional Lorenz system. Phys Rev Lett 91 (2003) 034101
55. Arena P., Caponetto R., Fortuna L., and Porto D. Bifurcation and chaos in noninteger order cellular neural networks. Int J Bifur Chaos 7 (1998) 1527-1539
56. Arena P., Fortuna L., and Porto D. Chaotic behavior in noninteger-order cellular neural networks. Phys Rev E 61 (2000) 776-781
57. Li C.G., and Chen G. Chaos and hyperchaos in fractional order Rössler equations. Physica A 341 (2004) 55-61
58. Li C.G., and Chen G. Chaos in the fractional order Chen system and its control. Chaos, Solitons & Fractals 22 (2004) 549-554
59. Li C.P., and Peng G.J. Chaos in Chen's system with a fractional order. Chaos, Solitons & Fractals 22 (2004) 443-450
60. Zaslavsky G.M. Chaos, fractional kinetics, and anomalous transport. Phys Rep 371 (2002) 461-580
61. Lu J.G. Chaotic dynamics and synchronization of fractional-order Arneodo's systems. Chaos, Solitons & Fractals 26 (2005) 1125-1133
62. Charef A., Sun H.H., Tsao Y.Y., and Onaral B. Fractal system as represented by singularity function. IEEE Trans Auto Control 37 (1992) 1465-1470