Complete synchronization and generalized synchronization of one-way coupled time-delay systems

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 68, Issue 3 2, 2003, Pages 362081-362085

  Zhan, Meng ^a   Wang, Xingang ^a   Gong, Xiaofeng ^a   Wei, G W ^a,b   Lai, C H ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; COUPLED CIRCUITS; LYAPUNOV METHODS; RESONANCE; SYNCHRONIZATION; SYSTEM STABILITY; SYSTEMS ANALYSIS;

DESYNCHRONIZATION; TIME-DELAY SYSTEMS;

DELAY CIRCUITS;

EID: 0242411812     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. A.S. Pikovsky, M.G. Rosenblum, and J. Kurths, Synchronization - A Unified Approach to Nonlinear Science (Cambridge University Press, Cambridge, England, 2001); L.M. Pecora, T.L. Carroll, G.A. Johnson, D.J. Mar, and J.F. Heagy, Chaos 7, 520 (1997).
2. A.S. Pikovsky, M.G. Rosenblum, and J. Kurths, Synchronization - A Unified Approach to Nonlinear Science (Cambridge University Press, Cambridge, England, 2001); L.M. Pecora, T.L. Carroll, G.A. Johnson, D.J. Mar, and J.F. Heagy, Chaos 7, 520 (1997).
3. L.M. Pecora and T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990); 80, 2109 (1998).
4. L.M. Pecora and T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990); 80, 2109 (1998).
5. J. Yang, G. Hu, and J. Xiao, Phys. Rev. Lett. 80, 496 (1998); M. Zhan, G. Hu, and J. Yang, Phys. Rev. E 62, 2963 (2000); G.W. Wei, M. Zhan, and C.-H. Lai, Phys. Rev. Lett. 89, 284103 (2002).
6. J. Yang, G. Hu, and J. Xiao, Phys. Rev. Lett. 80, 496 (1998); M. Zhan, G. Hu, and J. Yang, Phys. Rev. E 62, 2963 (2000); G.W. Wei, M. Zhan, and C.-H. Lai, Phys. Rev. Lett. 89, 284103 (2002).
7. J. Yang, G. Hu, and J. Xiao, Phys. Rev. Lett. 80, 496 (1998); M. Zhan, G. Hu, and J. Yang, Phys. Rev. E 62, 2963 (2000); G.W. Wei, M. Zhan, and C.-H. Lai, Phys. Rev. Lett. 89, 284103 (2002).
8. N.F. Rulkov, M.M. Sushchik, L.S. Tsimring, and H.D.I. Abarbanel, Phys. Rev. E 51, 980 (1995); L.M. Pecora, T.L. Carroll, and J.F. Heagy, ibid. 52, 3420 (1995); L. Kocarev and U. Parlitz, Phys. Rev. Lett. 76, 1816 (1996).
9. N.F. Rulkov, M.M. Sushchik, L.S. Tsimring, and H.D.I. Abarbanel, Phys. Rev. E 51, 980 (1995); L.M. Pecora, T.L. Carroll, and J.F. Heagy, ibid. 52, 3420 (1995); L. Kocarev and U. Parlitz, Phys. Rev. Lett. 76, 1816 (1996).
10. N.F. Rulkov, M.M. Sushchik, L.S. Tsimring, and H.D.I. Abarbanel, Phys. Rev. E 51, 980 (1995); L.M. Pecora, T.L. Carroll, and J.F. Heagy, ibid. 52, 3420 (1995); L. Kocarev and U. Parlitz, Phys. Rev. Lett. 76, 1816 (1996).
11. M.G. Rosenblum, A.S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996); A.S. Pikovsky, M.G. Rosenblum, G.V. Osipov, and J. Kurths, Physica D 104, 219 (1997); T. Yalcinkaya and Y.C. Lai, Phys. Rev. Lett. 79, 3885 (1997).
12. M.G. Rosenblum, A.S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996); A.S. Pikovsky, M.G. Rosenblum, G.V. Osipov, and J. Kurths, Physica D 104, 219 (1997); T. Yalcinkaya and Y.C. Lai, Phys. Rev. Lett. 79, 3885 (1997).
13. M.G. Rosenblum, A.S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996); A.S. Pikovsky, M.G. Rosenblum, G.V. Osipov, and J. Kurths, Physica D 104, 219 (1997); T. Yalcinkaya and Y.C. Lai, Phys. Rev. Lett. 79, 3885 (1997).
14. M.G. Rosenblem, A.S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
15. S. Rim, I. Kim, P. Kang, Y.-J. Park, and C-M. Kim, Phys. Rev. E 66, 015205 (2002); D. Pazo, M.A. Zaks, and J. Kurths, Chaos 13, 309 (2003); M. Zhan, G.W. Wei, and C.-H. Lai, Phys. Rev. E 65, 036202 (2002).
16. S. Rim, I. Kim, P. Kang, Y.-J. Park, and C-M. Kim, Phys. Rev. E 66, 015205 (2002); D. Pazo, M.A. Zaks, and J. Kurths, Chaos 13, 309 (2003); M. Zhan, G.W. Wei, and C.-H. Lai, Phys. Rev. E 65, 036202 (2002).
17. S. Rim, I. Kim, P. Kang, Y.-J. Park, and C-M. Kim, Phys. Rev. E 66, 015205 (2002); D. Pazo, M.A. Zaks, and J. Kurths, Chaos 13, 309 (2003); M. Zhan, G.W. Wei, and C.-H. Lai, Phys. Rev. E 65, 036202 (2002).
18. G. Perez and H. Cerdeira, Phys. Rev. Lett. 74, 1970 (1995); K.M. Short and A.T. Parker, Phys. Rev. E 58, 1159 (1998).
19. G. Perez and H. Cerdeira, Phys. Rev. Lett. 74, 1970 (1995); K.M. Short and A.T. Parker, Phys. Rev. E 58, 1159 (1998).
20. K. Kaneko, Theory and Applications of Coupled Map Lattices (Wiley, New York, 1993).
21. M.C. Mackey and L. Glass, Science 197, 287 (1977); J.D. Farmer, Physica D 4, 366 (1982); P. Grassberger and I. Procaccia, ibid. 9, 189 (1983).
22. M.C. Mackey and L. Glass, Science 197, 287 (1977); J.D. Farmer, Physica D 4, 366 (1982); P. Grassberger and I. Procaccia, ibid. 9, 189 (1983).
23. M.C. Mackey and L. Glass, Science 197, 287 (1977); J.D. Farmer, Physica D 4, 366 (1982); P. Grassberger and I. Procaccia, ibid. 9, 189 (1983).
24. S. Wang, J. Kuang, J. Li, Y. Luo, H. Lu, and G. Hu, Phys. Rev. E 66, 065202 (2002).
25. K. Pyragas, Phys. Rev. E 58, 3067 (1998).
26. M.J. Bunner and W. Just, Phys. Rev. E 58, R4072 (1998).
27. S. Boccaletti, D.L. Valladares, J. Kurths, D. Maza, and H. Mancini, Phys. Rev. E 61, 3712 (2000).
28. L.F. Shampine and S. Thompson, Appl. Numer. Math. 37, 441 (2001).
29. K. Pyragas, Phys. Rev. E 54, R4508 (1996); M.S. Vieira and A.J. Lichtenberg, ibid. 56, R3741 (1997).
30. K. Pyragas, Phys. Rev. E 54, R4508 (1996); M.S. Vieira and A.J. Lichtenberg, ibid. 56, R3741 (1997).
31. M.J. Bunner, T. Meyer, A. Kittel, and J. Parisi, Phys. Rev. E 56, 5083 (1997); R. Hegger, M.J. Bunner, H. Kantz, and A. Giaquinta, Phys. Rev. Lett. 81, 558 (1998); C. Zhou and C.-H. Lai, Phys. Rev. E 60, 320 (1999).
32. M.J. Bunner, T. Meyer, A. Kittel, and J. Parisi, Phys. Rev. E 56, 5083 (1997); R. Hegger, M.J. Bunner, H. Kantz, and A. Giaquinta, Phys. Rev. Lett. 81, 558 (1998); C. Zhou and C.-H. Lai, Phys. Rev. E 60, 320 (1999).
33. M.J. Bunner, T. Meyer, A. Kittel, and J. Parisi, Phys. Rev. E 56, 5083 (1997); R. Hegger, M.J. Bunner, H. Kantz, and A. Giaquinta, Phys. Rev. Lett. 81, 558 (1998); C. Zhou and C.-H. Lai, Phys. Rev. E 60, 320 (1999).
34. A. Namajunas, K. Pyragas, and A. Tamasevicius, Phys. Lett. A 201, 42 (1995).