The theorems of unsynchronizability and synchronization for coupled chaotic systems

International Journal of Nonlinear Sciences and Numerical Simulation

Volumn 8, Issue 1, 2007, Pages 101-112

  Ge, Zheng Ming ^a   Tsen, Pu Chien ^a  

^a NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

Chaos; Coupled chaotic systems; Synchronization; Unsynchronizablility

Indexed keywords

EID: 34250002513     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2007.8.1.101     Document Type: Article

References (24)

1. L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64(1990), 821.
2. R. He and P. G. Vaidya, Analysis and synthesis of synchronous periodic and chaotic systems, Phys. Rev. A 46(1992), 7387.
3. M. Ding and E. Ott, Enhancing synchronism of chaotic systems, Phys. Rev. E 49(1994), 945.
4. K. Murali and M. Lakshmanan, Drive-response scenario of chaos synchronization in identical nonlinear systems, Phys. Rev. E49(1994), 4882.
5. L. Kocarev, U. Parlitz and R. Brown, Robust synchronization of chaotic systems, Phys. Rev. E 61(2000), 3716.
6. T.-L. Liao and S.-H. Tsai, Adaptive synchronization of chaotic systems and its application to secure communications, Chaos, Solitons & Fractals, 11(2000), 1387
7. S. Chen and J. Lu, Synchronization of an uncertain unified chaotic system via adaptive control, Chaos, Solitons & Fractals, 14(2002), 643
8. Z. Li and D. Xu, A secure communication scheme using projective chaos synchronization, Chaos, Solitons & Fractals, 22(2004), 477
9. M. di Bernardo, A purely adaptive controller to synchronize and control chaotic systems, Phys. Lett. A 214(1996), 139.
10. Y.-G. Hong, H.-S. Qin and G.-R. Chen, Adaptive synchronization of chaotic systems via state or output feedback control, Int. J. Bifurcation and Chaos 11(2001), 1149.
11. J.-Q. Fang, Y.-G. Hong and G.-R. Chen, Switching manifold approach to chaos synchronization, Phys. Rev. E 59(1999), R2523.
12. X.-H. Yu and Y.-X. Song, Chaos synchronization via controlling partial state of chaotic systems, Int. J. Bifurcation and Chaos 11(2001), 1737.
13. Zheng-Ming Ge and W.-Y. Leu, Anti-control of chaos of two-degrees-of-freedom loudspeaker system and chaos synchronization of different order systems, Chaos, Solitons & Fractals, 20(2004), 503.
14. Zheng-Ming Ge and C.-C. Chen, Phase synchronization of coupled chaotic multiple time scales systems, Chaos, Solitons & Fractals, 20(2004), 639.
15. Zheng-Ming Ge and C.-M. Chang, Chaos synchronization and parameters identification of single time scale brushless DC motors, Chaos, Solitons & Fractals, 20(2004), 883.
16. Zheng-Ming Ge and W.-Y. Leu, Chaos synchronization and parameter identification for loudspeaker systems, Chaos, Solitons & Fractals, 21(2004), 1231.
17. C. Hua and X. Guan, Chaos Adaptive control for chaotic systems, Chaos, Solitons & Fractals, 22(2004), 55.
18. Y. Yu and S. Zhang, The synchronization of linearly bidirectional coupled chaotic systems, Chaos, Solitons & Fractals, 22(2004), 189.
19. C. Li and X. Liao, Complete and lag synchronization of hyperchaotic systems using small impulses, Chaos, Solitons & Fractals, 22(2004), 857.
20. Zheng-Ming Ge and Yen-Sheng Chen, Synchronization of unidirectional coupled chaotic systems via partial stability, Chaos, Solitons & Fractals, 21(2004), 101.
21. G Chen, T Ueta, Yet another chaotic attractor, Int. J. Bifurcation and Chaos 9(1999), 1465.
22. O. E. Rössler, An equation for continuous chaos, Phys. Lett. A 57(1976), 397.
23. Zheng-Ming Ge, Developing Theory of Motion Stability, Gau Lih Book Company, Taipei, 2001
24. T. M Apostol, Mathematical Analysis, Addison-Wesley, Reading, MA, 1957.