Persistent clusters in lattices of coupled nonidentical chaotic systems

Chaos

Volumn 13, Issue 1, 2003, Pages 165-178

  Belykh, I ^a   Belykh, V ^b   Nevidin, K ^b   Hasler, M ^a  

^a EPFL   (Switzerland)

^b Volga State Academy   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242668717     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1514202     Document Type: Article

References (56)

1. H. Fujisaka and T. Yamada, Prog. Theor. Phys. 69, 32 (1983); 72, 885 1984
2. H. Fujisaka and T. Yamada, Prog. Theor. Phys. 69, 32 (1983); 72, 885 1984
3. V.S. Afraimovich, N.M. Verichev, and M.I. Rabinovich, Izv. Vyssh. Uchebn. Zaved., Radiofiz. 29, 795 (1986).
4. L.M. Pecora and T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
5. J.F. Heagy, T.L. Carroll, and L.M. Pecora, Phys. Rev. E 50, 1874 (1994).
6. V.M. Belykh, N.N. Verichev, L.J. Kocarev, and L.O. Chua, in Chua's Circuit: A Paradigm for Chaos, edited by R.N. Madan (World Scientific, Singapore, 1993), pp. 325-335.
7. J.F. Heagy, L.M. Pecora, and T.L. Carroll, Phys. Rev. Lett. 74, 4185 (1995).
8. L.M. Pecora, T.L. Carroll, G.A. Johnson, D.J. Mar, and J.F. Heagy, Chaos 7, 520 (1997).
9. L.M. Pecora and T.L. Carroll, Phys. Rev. Lett. 80, 2109 (1998).
10. A.Yu. Pogromsky and H. Nvjmeijer, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 48, 152 (2001).
11. K. Kaneko, Physica D 41, 137 (1990); 54, 5 (1991); 55, 368 (1992); 75, 55 (1994).
12. K. Kaneko, Physica D 41, 137 (1990); 54, 5 (1991); 55, 368 (1992); 75, 55 (1994).
13. K. Kaneko, Physica D 41, 137 (1990); 54, 5 (1991); 55, 368 (1992); 75, 55 (1994).
14. K. Kaneko, Physica D 41, 137 (1990); 54, 5 (1991); 55, 368 (1992); 75, 55 (1994).
15. A. Sherman, Bull. Math. Biol. 56, 811 (1994).
16. V.N. Belykh and E. Mosekilde, Phys. Rev. E 54, 3196 (1996); F. Xie and G. Hu, ibid. 55, 79 (1997); D.H. Zanette and A.S. Mikhailov, ibid. 57, 276 (1998); M. Hasler, Yu. Maistrenko, and O. Popovych, ibid. 58, 6843 (1998).
17. V.N. Belykh and E. Mosekilde, Phys. Rev. E 54, 3196 (1996); F. Xie and G. Hu, ibid. 55, 79 (1997); D.H. Zanette and A.S. Mikhailov, ibid. 57, 276 (1998); M. Hasler, Yu. Maistrenko, and O. Popovych, ibid. 58, 6843 (1998).
18. V.N. Belykh and E. Mosekilde, Phys. Rev. E 54, 3196 (1996); F. Xie and G. Hu, ibid. 55, 79 (1997); D.H. Zanette and A.S. Mikhailov, ibid. 57, 276 (1998); M. Hasler, Yu. Maistrenko, and O. Popovych, ibid. 58, 6843 (1998).
19. V.N. Belykh and E. Mosekilde, Phys. Rev. E 54, 3196 (1996); F. Xie and G. Hu, ibid. 55, 79 (1997); D.H. Zanette and A.S. Mikhailov, ibid. 57, 276 (1998); M. Hasler, Yu. Maistrenko, and O. Popovych, ibid. 58, 6843 (1998).
20. J.R. Terry, K.S. Thornburg, Jr., D.J. DeShazer, G.D. Vanwiggeren, S. Zhu, P. Ashwin, and R. Roy, Phys. Rev. E 59, 4036 (1999).
21. V.N. Belykh, I.V. Belykh, and M. Hasler, Phys. Rev. E 62, 6332 (2000).
22. V.N. Belykh, I.V. Belykh, and E. Mosekilde, Phys. Rev. E 63, 036216 (2001).
23. V.N. Belykh, I.V. Belykh, K.V. Nevidin, and M. Hasler, Int. J. Bifurcation Chaos Appl. Sci. Eng. (to be published).
24. N.J. Balmforth, C. Pasquero, and A. Provenzale, Physica D 138, 1 (2000).
25. N.F. Rulkov, M.M. Suschik, L.S. Tsimring, and H.D.I. Abarbanel, Phys. Rev. E 51, 980 (1995); H.D. Abarbanel, N.F. Rulkov, and M.M. Sushik, ibid. 53, 4528 (1996); L. Kocarev and U. Parlitz, Phys. Rev. Lett. 76, 1816 (1996).
26. N.F. Rulkov, M.M. Suschik, L.S. Tsimring, and H.D.I. Abarbanel, Phys. Rev. E 51, 980 (1995); H.D. Abarbanel, N.F. Rulkov, and M.M. Sushik, ibid. 53, 4528 (1996); L. Kocarev and U. Parlitz, Phys. Rev. Lett. 76, 1816 (1996).
27. N.F. Rulkov, M.M. Suschik, L.S. Tsimring, and H.D.I. Abarbanel, Phys. Rev. E 51, 980 (1995); H.D. Abarbanel, N.F. Rulkov, and M.M. Sushik, ibid. 53, 4528 (1996); L. Kocarev and U. Parlitz, Phys. Rev. Lett. 76, 1816 (1996).
28. M.G. Rosenblum, A.S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).
29. M.G. Rosenblum, A.S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193
30. J.C. Alexander, J.A. Yorke, Z. You, and I. Kan, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 795 (1992); J.C. Alexander, B.R. Hunt, I. Kan, and J.A. Yorke, Ergod. Theory Dyn. Syst. 16, 651 (1996); Y.-C. Lai and C. Grebogi, Phys. Rev. Lett. 77, 5047 (1996); Y.-C. Lai and V. Andrade, Phys. Rev. E 64, 056228 (2001).
31. J.C. Alexander, J.A. Yorke, Z. You, and I. Kan, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 795 (1992); J.C. Alexander, B.R. Hunt, I. Kan, and J.A. Yorke, Ergod. Theory Dyn. Syst. 16, 651 (1996); Y.-C. Lai and C. Grebogi, Phys. Rev. Lett. 77, 5047 (1996); Y.-C. Lai and V. Andrade, Phys. Rev. E 64, 056228 (2001).
32. J.C. Alexander, J.A. Yorke, Z. You, and I. Kan, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 795 (1992); J.C. Alexander, B.R. Hunt, I. Kan, and J.A. Yorke, Ergod. Theory Dyn. Syst. 16, 651 (1996); Y.-C. Lai and C. Grebogi, Phys. Rev. Lett. 77, 5047 (1996); Y.-C. Lai and V. Andrade, Phys. Rev. E 64, 056228 (2001).
33. J.C. Alexander, J.A. Yorke, Z. You, and I. Kan, Int. J. Bifurcation Chaos Appl. Sci. Eng. 2, 795 (1992); J.C. Alexander, B.R. Hunt, I. Kan, and J.A. Yorke, Ergod. Theory Dyn. Syst. 16, 651 (1996); Y.-C. Lai and C. Grebogi, Phys. Rev. Lett. 77, 5047 (1996); Y.-C. Lai and V. Andrade, Phys. Rev. E 64, 056228 (2001).
34. P. Ashwin, J. Buescu, and I. Stewart, Phys. Lett. A 193, 126 (1994); Nonlinearity 9, 703 (1996); J.F. Heagy, T.L. Carroll, and L.M. Pecora, Phys. Rev. E 52, R1253 (1995).
35. P. Ashwin, J. Buescu, and I. Stewart, Phys. Lett. A 193, 126 (1994); Nonlinearity 9, 703 (1996); J.F. Heagy, T.L. Carroll, and L.M. Pecora, Phys. Rev. E 52, R1253 (1995).
36. L. Yu, E. Ott, and Q. Chen, Physica D 53, 102 (1992); N. Platt, E.A. Spiegel, and C. Tresser, Phys. Rev. Lett. 70, 279 (1993); Y.-C. Lai and C. Grebogi, Phys. Rev. E 52, R3313 (1995).
37. L. Yu, E. Ott, and Q. Chen, Physica D 53, 102 (1992); N. Platt, E.A. Spiegel, and C. Tresser, Phys. Rev. Lett. 70, 279 (1993); Y.-C. Lai and C. Grebogi, Phys. Rev. E 52, R3313 (1995).
38. L. Yu, E. Ott, and Q. Chen, Physica D 53, 102 (1992); N. Platt, E.A. Spiegel, and C. Tresser, Phys. Rev. Lett. 70, 279 (1993); Y.-C. Lai and C. Grebogi, Phys. Rev. E 52, R3313 (1995).
39. R.E. Mirollo and S.H. Stewart, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 50, 1645 (1990).
40. S.H. Strogatz and I. Stewart, Sci. Am. 269, 102 (1993).
41. V.I. Nekorkin, V.B. Kazantsev, M.G. Velarde, and L.O. Chua, Phys. Rev. E 58, 1764 (1998).
42. V.B. Kazantsev, V.I. Nekorkin, U.V. Artyuhin, and M.G. Velarde, Phys. Rev. E 63, 016212 (2001).
43. M. Hasler and Yu.L. Maistrenko, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 44, 856 (1997).
44. G.A. Johnson, D.J. Mar, T.L. Carroll, and L.M. Pecora, Phys. Rev. Lett. 80, 3956 (1998).
45. Z. Liu, S. Chen, and B. Hu, Phys. Rev. E 59, 2817 (1999).
46. S. Yanchuk, Yu. Maistrenko, B. Lading, and E. Mosekilde, Int. J. Bifurcation Chaos Appl. Sei. Eng. 10, 2629 (2000).
47. K. Josić, Nonlinearity 13, 1321 (2000).
48. V.S. Afraimovich, S.N. Chow, and J.K. Hale, Physica D 103, 442 (1997).
49. J.K. Hale, J. Dyn. Diff. Eq. 9, 1 (1997).
50. V.S. Afraimovich and W.W. Lin, Dyn. Stab. Syst. 13, 237 (1998).
51. C.H. Chiu, W.W. Lin, and C.C. Peng, Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 2717 (2000).
52. N. Fenichel, Indiana Univ. Math. J. 21, 193 (1971).
53. L.P. Shilnikov, A.L. Shilnikov, D.V. Turaev, and L.O. Chua, Methods of Qualitative Theory in Nonlinear Dynamics (Part I), World Scientific Series on Nonlinear Science, Series A 4 (World Scientific, Singapore, 1998).
54. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors (Springer, New York, 1982).
55. G.V. Osipov, A. Pikovsky, M. Rosenblum, and J. Kurths, Phys. Rev. E 55, 2353 (1997); Z. Liu and B. Hu, Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, 3137 (2001).
56. G.V. Osipov, A. Pikovsky, M. Rosenblum, and J. Kurths, Phys. Rev. E 55, 2353 (1997); Z. Liu and B. Hu, Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, 3137 (2001).