Experimental verification of a four-dimensional chua's system and its fractional order chaotic attractors

International Journal of Bifurcation and Chaos

Volumn 19, Issue 8, 2009, Pages 2473-2486

  Liu, Ling ^a   Liu, Chongxin ^a   Zhang, Yanbin ^a  

^a NONE

Author keywords

Chaotic attractor; Circuit implementation; Dynamical behaviors; Four dimensional Chua's system; Fractional order circuit implementation

Indexed keywords

APPROXIMATION THEORY; CHAOS THEORY; CIRCUIT OSCILLATIONS; CONTINUOUS TIME SYSTEMS; DYNAMICAL SYSTEMS; DYNAMICS; HARDWARE; LYAPUNOV METHODS; OPERATIONAL AMPLIFIERS;

CHAOTIC ATTRACTORS; CHUA'S SYSTEM; CIRCUIT IMPLEMENTATION; DYNAMICAL BEHAVIORS; FRACTIONAL-ORDER CIRCUIT;

CHAOTIC SYSTEMS;

EID: 70449397800     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127409024256     Document Type: Article

References (44)

1. Ahmad, M. & Sprott, J. C. [2003] "Chaos in fractionalorder autonomous nonlinear systems," Chaos Solit. Fract. 16, 339-351.
2. Banerjee, S. [1997] "Coexisting attractors, chaotic saddles, and fractal basins in a power electronic circuit," IEEE Trans. Circuits Syst.-I 44, 847-849.
3. Banerjee, S. & Verghese, G. C. [2001] Nonlinear Phenomena in Power Electronics: Attractors, Bifurcations, Chaos, and Nonlinear Control Piscataway (IEEE Press, NJ).
4. Carlson, G. E. & Halijak, C. A. [1964] "Approximation of fractional capacitors (1/s)1/n by a regular Newton process," IRE Trans. Circ. Th. 11, 210-213.
5. Charef, A., Sun, H., Tsao, Y. & Onaral, B. [1992] "Fractal system as represented by singularity function," IEEE Trans. Automat. Contr. 37, 1465-1470.
6. Chen, G. & Ueta, T. [1999] "Yet another chaotic attractor," Int. J. Bifurcation and Chaos 9, 1465-1466.
7. Chua, L. O., Komuro, M. & Matsumoto, T. [1986] "The double scroll family," IEEE Trans. Circuits Syst.-I 33, 1073-1118.
8. Chua, L. O. & Lin, G. [1990] "Canonical realization of Chua's circuit family," IEEE Trans. Circuits Syst. 37, 885-902.
9. Chua, L. O. [1993] "Global unfolding of Chua's circuit," IEICE Trans. Fund. E76-A, 704-734.
10. Gao, T., Chen, Z., Yuan, Z. & Chen, G. [2006] "A hyperchaos generated from Chen's system," Int. J. Mod. Phys. C 17, 471-478.
11. Gao, T., Chen, G., Chen, Z. & Cang, S. [2007] "The generation and circuit implementation of a new hyperchaos based upon Lorenz system," Phys. Lett. A 361, 78-86.
12. Grigorenko, I. & Grigorenko, E. [2004] "Chaotic dnamics of the fractional Lorenz system," Phys. Rev. Lett. 91, 101-104.
13. Hartley, T. T., Lorenzo, C. F. & Qammer, H. K. [1995] "Chaos in a fractional order Chua's system," IEEE Trans. Circuits Syst.-I 42, 485-490.
14. Kapitaniak, T. [1992] Chaotic Oscillators: Theory and Applications (World Scientific, Singapore).
15. Kapitaniak, T., Chua, L. O. & Zhong, G. [1994] "Experimental hyperchaos in coupled Chua's circuits," IEEE Trans. Circuits Syst.-I 41, 499-503.
16. Li, C. & Chen, G. [2004a] "Chaos and hyperchaos in the fractional-order Rössler equations," Physica A 29, 441-444.
17. Li, C. & Chen, G. [2004b] "Chaos in the fractional order Chen system and its control," Chaos Solit. Fract. 22, 549-554.
18. Li, C. & Peng, G. [2004] "Chaos in Chen's system with a fractional order," Chaos Solit. Fract. 22, 443-450.
19. Liu, C., Liu, T., Liu, L. & Liu, K. [2004] "A new chaotic attractor," Chaos Solit. Fract. 22, 1031-1038.
20. Liu, L., Su, Y. & Liu, C. [2006] "A new chaotic system and its circuit emulation," Acta Phys. Sin. 55, 3933-3937 (in Chinese).
21. Liu, L., Liu, C. & Zhang, Y. [2007] "Experimental con- firmation of a modified Lorenz system," Chin. Phys. Lett. 24, 2756-2758.
22. Liu, L., Su, Y. & Liu, C. [2007] "Experimental confirmation of a new reversed butter.y-shaped attractor," Chin. Phys. 16, 1897-1900.
23. Lorenz, E. N. [1963] "Deterministic nonperiodic flow," J. Atmos. Sci. 20, 130-141.
24. Lü, J. & Chen, G. [2002] "A new chaotic attractor coined," Int. J. Bifurcation and Chaos 12, 659-661.
25. Lü, J., Yu, X. & Chen, G. [2003] "Generating chaotic attractors with multiple merged basins of attraction: A switching piecewise-linear control approach," IEEE Trans. Circuits Syst.-I 50, 198-207.
26. Lu, J.&Liu,C. [2007] "Realization of fractional-order Liu chaotic system by circuit," Chin. Phys. 16, 1586-1590. (Pubitemid 46887492)
27. Matsumoto, T., Chua, L. O. & Kobayashi, K. [1986] "Hyperchaos: Laboratory experiment and numerical confirmation," IEEE Trans. Circuits Syst.-I 33, 1143-1147.
28. Oldham, K. B. & Spanier, J. [1974] The Fractional Calculus (Academic Press, NY).
29. Podlubny, I., Komuro, M. & Matsumoto, T. [1999] Fractional Differential Equations (Academic Press, NY, US).
30. Qi, G. & Chen, G. [2006] "Analysis and circuit implementation of a new 4D chaotic system," Phys. Lett. A 352, 386-397.
31. Robinson, R. C. [2004] An Introduction to Dynamical Systems: Continuous and Discrete (Prentice Hall, NY, US).
32. Rössler, O. E. [1976] "An equation for continuous chaos," Phys. Lett. A 57, 397-398.
33. Sun, H., Abdelwahab, A. A. & Onaral, B. [1984] "Linear approximation of transfer function with a pole of fractional order," IEEE Trans. Automat. Contr. AC-29, 441-444.
34. Tama¢sevi¢cius, A., Namaj̀unas, A. & ¢Cenys, A. [1996] "Simple 4D chaotic oscillator," Electron. Lett. 32, 957-958.
35. Wajdi, M. A. & Ahmad, M. H. [2003] "On nonlinear control design for autonomous chaotic systems of integer and fractional orders," Chaos Solit. Fract. 18, 693-701.
36. Wang, F. & Liu, C. [2006] "Hyperchaos evolved from the Liu chaotic system," Chin. Phys. 15, 963-968.
37. Wang, X. & Wang, M. [2007] "Dynamic analysis of the fractional-order Liu system and its synchronization," Chaos 17, 033106-33111
38. Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. [1985] "Determining Lyapunov exponents from a time series," Physica D 160, 285-317.
39. Wu, S. [1987] "Chua's circuit family," Proc. IEEE 75, 1022-1032.
40. Yalcin, M. E., Suvkens, J. A. K. & Vandewalle, J. [2000] "Experimental confirmation of 3- and 5-scroll attractors from a generalized Chua's circuit," IEEE Trans. Circuits Syst. 47, 425-429.
41. Yang, X., Li, Q. & Chen, G. [2003] "A twin-star hyperchaotic attractor and its circuit implementation," Int. J. Circuits Th. Appl. 31, 637-640.
42. Yang, Y., Duan, Z. & Huang, L. [2007] "Robust dichotomy analysis and synthesis with application to an extended Chua's circuit," IEEE Trans. Circuits Syst.-I 54, 2078-2086.
43. Yu, S., Lü, J., Leung, H. & Chen, G. [2005] "Design and implementation of n-scroll chaotic attractors from a general jerk circuit," IEEE Trans. Circuits Syst.-I 52, 1459-1475.
44. Yu, S., Lü, J. & Chen, G. [2007] "Theoretical design and circuit implementation of multidirectional multi-torus chaotic attractors," IEEE Trans. Circuits Syst.-I 54, 2087-2098.