Global Effect of Transverse Bifurcations in Coupled Chaotic Systems

Journal of the Korean Physical Society

Volumn 43, Issue 2, 2003, Pages 193-201

  Lim, Woochang ^a   Kim, Sang Yoon ^a  

^a Kangwon National University   (South Korea)

Author keywords

Chaos synchronization; Transverse bifurcation

Indexed keywords

EID: 0042416736     PISSN: 03744884     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. H. Fujisaka and T. Yamada, Prog. Theor. Phys. 69, 32 (1983).
2. A. S. Pikovsky, Z. Phys. B: Condens, Matter 50, 149 (1984).
3. V. S. Afraimovich, N. N. Verichev and M. I. Rabinovich, Radiophys. Quantum Electron. 29, 795 (1986).
4. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
5. K. M. Cuomo and A. V. Oppenheim, Phys. Rev. Lett. 71, 65 (1993); L. Kocarev, K. S. Halle, K. Eckert, L. O. Chua and U. Parlitz, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 973 (1992); L. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995); N. F. Rulkov, Chaos 6, 262 (1996).
6. K. M. Cuomo and A. V. Oppenheim, Phys. Rev. Lett. 71, 65 (1993); L. Kocarev, K. S. Halle, K. Eckert, L. O. Chua and U. Parlitz, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 973 (1992); L. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995); N. F. Rulkov, Chaos 6, 262 (1996).
7. K. M. Cuomo and A. V. Oppenheim, Phys. Rev. Lett. 71, 65 (1993); L. Kocarev, K. S. Halle, K. Eckert, L. O. Chua and U. Parlitz, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 973 (1992); L. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995); N. F. Rulkov, Chaos 6, 262 (1996).
8. K. M. Cuomo and A. V. Oppenheim, Phys. Rev. Lett. 71, 65 (1993); L. Kocarev, K. S. Halle, K. Eckert, L. O. Chua and U. Parlitz, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 973 (1992); L. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995); N. F. Rulkov, Chaos 6, 262 (1996).
9. P. Ashwin, J. Buescu and I. Stewart, Nonlinearity 9, 703 (1996).
10. B. R. Hunt and E. Ott, Phys. Rev. Lett. 76, 2254 (1996); Phys. Rev. E 54, 328 (1996).
11. B. R. Hunt and E. Ott, Phys. Rev. Lett. 76, 2254 (1996); Phys. Rev. E 54, 328 (1996).
12. Y.-C. Lai, C. Grebogi, J. A. Yorke and S. C. Venkataramani, Phys. Rev. Lett. 77, 55 (1996).
13. V. Astakhov, A. Shabunin, T. Kapitaniak and V. Anishchenko, Phys. Rev. Lett. 79, 1014 (1997).
14. Yu. L. Maistrenko, V. L. Maistrenko, A. Popovich and E. Mosekilde, Phys. Rev. E 57, 2713 (1998); 60, 2817 (1999).
15. Yu. L. Maistrenko, V. L. Maistrenko, A. Popovich and E. Mosekilde, Phys. Rev. E 57, 2713 (1998); 60, 2817 (1999).
16. Yu, L. Maistrenko, V. L. Maistrenko, A. Popovich and E. Mosekilde, Phys. Rev. Lett. 80, 1638 (1998); G.-I. Bischi and L. Gardini, Phys. Rev. E 58, 5710 (1998).
17. Yu, L. Maistrenko, V. L. Maistrenko, A. Popovich and E. Mosekilde, Phys. Rev. Lett. 80, 1638 (1998); G.-I. Bischi and L. Gardini, Phys. Rev. E 58, 5710 (1998).
18. O. Popovych, Yu. L. Maistrenko, E. Moskilde, A. Pikovsky and J. Kurths, Phys. Lett. A 275, 401 (2000); Phys. Rev. E 63, 036201 (2001).
19. O. Popovych, Yu. L. Maistrenko, E. Moskilde, A. Pikovsky and J. Kurths, Phys. Lett. A 275, 401 (2000); Phys. Rev. E 63, 036201 (2001).
20. S.-Y. Kim and W. Lim, Phys. Rev. E 63, 026217 (2001); S.-Y. Kim, W. Lim and Y. Kim, Prog. Theor. Phys. 105, 187 (2001); S.-Y. Kim and W. Lim, Phys. Rev. E 64, 016211 (2001); W. Lim, S.-Y. Kim and Y. Kim, J. Korean Phys. Soc. 38, 532 (2001).
21. S.-Y. Kim and W. Lim, Phys. Rev. E 63, 026217 (2001); S.-Y. Kim, W. Lim and Y. Kim, Prog. Theor. Phys. 105, 187 (2001); S.-Y. Kim and W. Lim, Phys. Rev. E 64, 016211 (2001); W. Lim, S.-Y. Kim and Y. Kim, J. Korean Phys. Soc. 38, 532 (2001).
22. S.-Y. Kim and W. Lim, Phys. Rev. E 63, 026217 (2001); S.-Y. Kim, W. Lim and Y. Kim, Prog. Theor. Phys. 105, 187 (2001); S.-Y. Kim and W. Lim, Phys. Rev. E 64, 016211 (2001); W. Lim, S.-Y. Kim and Y. Kim, J. Korean Phys. Soc. 38, 532 (2001).
23. S.-Y. Kim and W. Lim, Phys. Rev. E 63, 026217 (2001); S.-Y. Kim, W. Lim and Y. Kim, Prog. Theor. Phys. 105, 187 (2001); S.-Y. Kim and W. Lim, Phys. Rev. E 64, 016211 (2001); W. Lim, S.-Y. Kim and Y. Kim, J. Korean Phys. Soc. 38, 532 (2001).
24. C. Mira, L. Gardini, A. Barugola and J.-C. Cathala, Chaotic Dynamics in Two-Dimensional Noninvertible Maps (World Scientific, Singapore, 1996); R. H. Abraham, L. Gardini and C. Mira, Chaos in Discrete Dynamical Systems (Springer, New York, 1997).
25. C. Mira, L. Gardini, A. Barugola and J.-C. Cathala, Chaotic Dynamics in Two-Dimensional Noninvertible Maps (World Scientific, Singapore, 1996); R. H. Abraham, L. Gardini and C. Mira, Chaos in Discrete Dynamical Systems (Springer, New York, 1997).
26. P. Ashwin, J. Buescu and I. Stewart, Phys. Lett. A 193, 126 (1994); J. F. Heagy, T. L. Carroll and L. M. Pecora, Phys. Rev. E 52, 1253 (1995).
27. P. Ashwin, J. Buescu and I. Stewart, Phys. Lett. A 193, 126 (1994); J. F. Heagy, T. L. Carroll and L. M. Pecora, Phys. Rev. E 52, 1253 (1995).
28. S. C. Venkataramani, B. R. Hunt, E. Ott, D. J. Gauthier and J. C. Bienfang, Phys. Rev. Lett. 77, 5361 (1996); S. C. Venkataramani, B. R. Hunt and E. Ott, Phys. Rev. E 54, 1346 (1996).
29. S. C. Venkataramani, B. R. Hunt, E. Ott, D. J. Gauthier and J. C. Bienfang, Phys. Rev. Lett. 77, 5361 (1996); S. C. Venkataramani, B. R. Hunt and E. Ott, Phys. Rev. E 54, 1346 (1996).
30. J.-H. Cho, D.-U. Hwang, C.-M. Kim and Y.-J. Park, J. Korean Phys. Soc. 39, 378 (2001).
31. J. C. Alexander, J. A. Yorke, Z. You and I. Kan, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 795 (1992); E. Ott, J. C. Sommerer, J. C. Alexander, I. Kan and J. A. Yorke, Phys, Rev. Lett. 71, 4134 (1993); J. C. Sommerer and E. Ott, Nature (London) 365, 136 (1993); E. Ott, J. C. Alexander, I. Kan, J. C. Sommerer and J. A. Yorke, Physica D 76, 384 (1994); J. F. Heagy, T. L. Carroll and L. M. Pecora, Phys. Rev. Lett. 73, 3528 (1994).
32. J. C. Alexander, J. A. Yorke, Z. You and I. Kan, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 795 (1992); E. Ott, J. C. Sommerer, J. C. Alexander, I. Kan and J. A. Yorke, Phys, Rev. Lett. 71, 4134 (1993); J. C. Sommerer and E. Ott, Nature (London) 365, 136 (1993); E. Ott, J. C. Alexander, I. Kan, J. C. Sommerer and J. A. Yorke, Physica D 76, 384 (1994); J. F. Heagy, T. L. Carroll and L. M. Pecora, Phys. Rev. Lett. 73, 3528 (1994).
33. J. C. Alexander, J. A. Yorke, Z. You and I. Kan, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 795 (1992); E. Ott, J. C. Sommerer, J. C. Alexander, I. Kan and J. A. Yorke, Phys, Rev. Lett. 71, 4134 (1993); J. C. Sommerer and E. Ott, Nature (London) 365, 136 (1993); E. Ott, J. C. Alexander, I. Kan, J. C. Sommerer and J. A. Yorke, Physica D 76, 384 (1994); J. F. Heagy, T. L. Carroll and L. M. Pecora, Phys. Rev. Lett. 73, 3528 (1994).
34. J. C. Alexander, J. A. Yorke, Z. You and I. Kan, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 795 (1992); E. Ott, J. C. Sommerer, J. C. Alexander, I. Kan and J. A. Yorke, Phys, Rev. Lett. 71, 4134 (1993); J. C. Sommerer and E. Ott, Nature (London) 365, 136 (1993); E. Ott, J. C. Alexander, I. Kan, J. C. Sommerer and J. A. Yorke, Physica D 76, 384 (1994); J. F. Heagy, T. L. Carroll and L. M. Pecora, Phys. Rev. Lett. 73, 3528 (1994).
35. J. C. Alexander, J. A. Yorke, Z. You and I. Kan, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 795 (1992); E. Ott, J. C. Sommerer, J. C. Alexander, I. Kan and J. A. Yorke, Phys, Rev. Lett. 71, 4134 (1993); J. C. Sommerer and E. Ott, Nature (London) 365, 136 (1993); E. Ott, J. C. Alexander, I. Kan, J. C. Sommerer and J. A. Yorke, Physica D 76, 384 (1994); J. F. Heagy, T. L. Carroll and L. M. Pecora, Phys. Rev. Lett. 73, 3528 (1994).
36. A. Jalnine and S.-Y. Kim, Phys. Rev. E 65, 026210 (2002); S.-Y. Kim, W. Lim, A. Jalnine and S. P. Kuznetsov, Phys. Rev. E 67, 016217 (2003).
37. A. Jalnine and S.-Y. Kim, Phys. Rev. E 65, 026210 (2002); S.-Y. Kim, W. Lim, A. Jalnine and S. P. Kuznetsov, Phys. Rev. E 67, 016217 (2003).
38. E. Ott and J. C. Sommerer, Phys. Lett. A 188, 39 (1994); Y. Nagai and Y.-C. Lai, Phys. Rev. E 56, 4031 (1997).
39. E. Ott and J. C. Sommerer, Phys. Lett. A 188, 39 (1994); Y. Nagai and Y.-C. Lai, Phys. Rev. E 56, 4031 (1997).