Some impulsive synchronization criterions for coupled chaotic systems via unidirectional linear error feedback approach

Chaos, Solitons and Fractals

Volumn 19, Issue 5, 2004, Pages 1049-1055

  Sun, Jitao ^a   Zhang, Yinping ^a   Qiao, Fei ^a   Wu, Qidi ^a  

^a TONGJI UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; FEEDBACK; THEOREM PROVING;

LINEAR ERROR FEEDBACK;

CHAOS THEORY;

EID: 0141859734     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(03)00264-9     Document Type: Article

References (41)

1. Pecora L.M., Carroll T.L. Synchronization in chaotic systems. Phys. Rev. Lett. 64(8):1990;821-824.
2. Carroll T.L., Pecora L.M. Synchronization chaotic circuits. IEEE Trans. Circ. Syst. 38(4):1991;453-456.
3. Chen G., Dong X. From Chaos to order: Methodologies, Perspectives and Applications. 1998;World Scientific, Singapore.
4. Suykens J.A.K., Yang T., Chua L.O. Impulsive synchronization of chaotic Lur'e systems by measurement feedback. Int. J. Bifurcat. Chaos. 8(6):1998;1371-1381.
5. Ushio T. Synthesis of synchronized chaotic systems based on observers. Int. J. Bifurcat. Chaos. 9(3):1999;541-546.
6. Blazejczky-Okolewska B., Brindley J., Czolczynski K., Kapitaniak T. Antiphase synchronization of chaos by noncontinuous coupling: two impacting oscillators. Chaos, Solitons & Fractals. 12(10):2001;1823-1826.
7. Bai E.-W., Lonngren K.E., Sprott J.C. On the synchronization of a class of electronic circuits that exhibit chaos. Chaos, Solitons & Fractals. 13(7):2002;1515-1521.
8. Gong X., Lai C.H. On the synchronization of different chaotic oscillators. Chaos, Solitons & Fractals. 11(8):2000;1231-1235.
9. Krawiecki A., Sukiennicki A. Generalizations of the concept of marginal synchronization of chaos. Chaos, Solitons & Fractals. 11(9):2000;1445-1458.
10. Liao T.L., Tsai S.H. Adaptive synchronization of chaotic systems and its application to secure communications. Chaos, Solitons & Fractals. 11(9):2000;1387-1396.
11. Sun J.T., Zhang Y.P., Wu Q.D. Impulsive control for the stabilization and synchronization of Lorenz systems. Phys. Lett. A. 298(2):2002;153-160.
12. Li Z.G., Wen C.Y., Soh Y.C. Analysis and design of impulsive control systems. IEEE Trans. Automat. Contr. 46(6):2001;894-903.
13. Sun J.T., Zhang Y.P., Wu Q.D. Less conservative conditions for asymptotic stability of impulsive control systems. IEEE Trans. Automat. Contr. 48(5):2003;829-831.
14. Sun J.T., Zhang Y.P., Wang L., Wu Q.D. Impulsive robust control of uncertain Luré systems. Phys. Lett. A. 304:2002;130-135.
15. Sun JT, Zhang YP. Impulsive control of a nuclear spin generator, J. Comput. Appl. Math., in press.
16. Chen G., Dong X. From chaos to order - Perspectives and methodologies in controlling nonlinear dynamical systems. Int. J. Bifurcat. Chaos. 3(8):1993;1363-1409.
17. Chua L.O., Yang T., Zhong G.Q., Wu C.W. Adaptive synchronization of Chua's oscillators. Int. J. Bifurcat. Chaos. 6(1):1996;189-201.
18. Hunt E.R., Johnson G. Keeping chaos at bay. IEEE Spectrum. 1993;32-36.
19. Ott E., Grebogi C., Yorke J.A. Controlling chaos. Phys. Rev. Lett. 64:1990;1196-1199.
20. Pyragas K. Continuous control of chaos by self-controlling feedback. Phys. Lett. A. 170:1992;421-428.
21. Kapitaniak T., Sekieta M., Ogorzalek M. Monotone synchronization of chaos. Int. J. Bifurcat. Chaos. 6(1):1996;211-217.
22. Kocarev L., Parlitz U. Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. Phys. Rev. Lett. 76:1996;1816-1819.
23. Grassi G., Mascolo S. Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal. IEEE Trans. Circ. Syst. I. 44(10):1997;1011-1014.
24. Grassi G., Mascolo S. Synchronizing high dimensional chaotic systems via eigenvalue placement with application to cellular neural networks. Int. J. Bifurcat. Chaos. 9(4):1999;705-711.
25. Liu F., Ren Y., Shan X., Qiu Z. A linear feedback synchronization theorem for a class of chaotic systems. Chaos, Solitons & Fractals. 13(4):2002;723-730.
26. Lü J., Zhou T., Zhang S. Chaos synchronization between linearly coupled chaotic systems. Chaos, Solitons & Fractals. 14(4):2002;529-541.
27. Jiang G.P., Tang K.S., Chen G.R. A simple global synchronization criterion for coupled chaotic systems. Chaos, Solitons & Fractals. 15:2003;925-935.
28. Sun J.T., Zhang Y.P. Some simple global synchronization criterions for coupled time-varying chaotic systems. Chaos, Solitons & Fractals. 19:2004;93-98.
29. Sun JT. Some global synchronization criterions for coupled delay-systems via unidirectional linear error feedback approach. Chaos, Solitons & Fractals, in press.
30. Yang T. Impulsive control. IEEE Trans. Automat. Contr. 44(5):1999;1081-1083.
31. Lakshmikantham V., Bainov D., Simeonov P.S. Theory of Impulsive Differential Equations. 1989;World Scientific, Singapore.
32. Bainov D., Simeonov P.S. System with Impulse Effect: Stability, Theory and Applications. 1989;Hslsted, New York.
33. Samoilenko A.M., Perestyuk N.A. Impulsive Differential Equations. 1995;World Scientific, Singapore.
34. Schweizer J., Kennedy M.P. Predictive Poincare control: a control theory for chaotic systems. Phys. Rev. E. 52(5):1995;4865-4876.
35. Stojanovski T., Kocarev L., Parlitz U. Driving and synchronizing by chaotic impulses. Phys. Rev. E. 43(9):1996;782-785.
36. Sun J.T., Zhang Y.P. Impulsive control of Rössler systems. Phys. Lett. A. 306:2003;306-312.
37. Bainov D., Kolev D., Motreanu D. Blow-up solutions for degenerate impulsive parabolic models. PanAmerican Math. J. 11(2):2001;81-94.
38. Yang T. Impulsive Control Theory. 2001;Springer-Verlag, Berlin.
39. Yang T. Impulsive Systems and Control: Theory and Application. 2001;Nova Science Publishers.
40. Bainov D., Kolev D., Nakagawa K. Blow-up property of the solutions of an impulsive reaction-diffusion model. Commun. Appl. Anal. 7(3):2003;359-367.
41. Shil'nikov L.P. Chua's circuit: rigorous results and future problems. Int. J. Bifurcat. Chaos. 4(3):1994;489-519.