Inducing coherence in networks of bistable maps by varying the interaction range

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

Volumn 69, Issue 2 2, 2004, Pages

  Lind, Pedro G ^a,b,c   Corte Real, João ^b,c   Gallas, Jason A C ^a,b,c,d  

^a FEDERAL UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

^b UNIVERSITY OF LISBON   (Portugal)

^c UNIVERSITY OF ÉVORA   (Portugal)

^d UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; EIGENVALUES AND EIGENFUNCTIONS; ELECTRIC NETWORK TOPOLOGY; FEEDBACK; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; SEMICONDUCTOR LASERS;

BISTABLE MAPS; COHERENCE STATES; COUPLING STRENGTH; FREE TUNABLE PARAMETERS; GLOBAL COUPLING; INTERACTION RANGE;

COUPLED CIRCUITS;

EID: 37649026490     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.69.026209     Document Type: Article

References (45)

1. A. Uchida, T. Matsuura, S. Kinugawa, and S. Yoshimori, Phys. Rev. E 65, 066212 (2002); J.R. Terry, K.S. Thornburg, Jr., D.J. DeShazer, G.D. VanWiggeren, S. Zhu, P. Ashwin, and R. Roy, ibid. 59, 4036 (1999).
2. A. Uchida, T. Matsuura, S. Kinugawa, and S. Yoshimori, Phys. Rev. E 65, 066212 (2002); J.R. Terry, K.S. Thornburg, Jr., D.J. DeShazer, G.D. VanWiggeren, S. Zhu, P. Ashwin, and R. Roy, ibid. 59, 4036 (1999).
3. L. Faoro, J. Siewert, and R. Fazio, Phys. Rev. Lett. 90, 028301 (2003); J.A. Acebrón, A. Perales, and R. Spigler, Phys. Rev. E 64, 016218 (2001).
4. L. Faoro, J. Siewert, and R. Fazio, Phys. Rev. Lett. 90, 028301 (2003); J.A. Acebrón, A. Perales, and R. Spigler, Phys. Rev. E 64, 016218 (2001).
5. D.A. Smirnov, B.P. Bezruchko, and Y.P. Seleznev, Phys. Rev. E 65, 026205 (2002); G. de Vries, ibid. 64, 051914 (2001).
6. D.A. Smirnov, B.P. Bezruchko, and Y.P. Seleznev, Phys. Rev. E 65, 026205 (2002); G. de Vries, ibid. 64, 051914 (2001).
7. M. Barahona and L. Pecora, Phys. Rev. Lett. 89, 054101 (2002).
8. S. Strogatz, Sync: The Emerging Science of Spontaneous Order (Hyperion, New York, 2003).
9. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization - A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001).
10. S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladares, and C.S. Zhou, Phys. Rep. 366, 1 (2002).
11. K. Kaneko and I. Tsuda, Complex Systems: Chaos and Beyond (Springer-Verlag, New York, 2000); Theory and Applications of Coupled Map Lattices, edited by K. Kaneko (Wiley, Chichester, 1993).
12. K. Kaneko and I. Tsuda, Complex Systems: Chaos and Beyond (Springer-Verlag, New York, 2000); Theory and Applications of Coupled Map Lattices, edited by K. Kaneko (Wiley, Chichester, 1993).
13. D.J. Watts and S.H. Strogatz, Nature (London) 393, 440 (1998); S.H. Strogatz, ibid. 410, 268 (2001).
14. D.J. Watts and S.H. Strogatz, Nature (London) 393, 440 (1998); S.H. Strogatz, ibid. 410, 268 (2001).
15. A.C. Vladimirov, G. Kozyreff, and P. Mandel, Europhys. Lett. 61, 613 (2003).
16. R.F. Cancho, C. Janssen, and R.V. Solé, Phys. Rev. E 64, 046119 (2001).
17. P. Svenson and D.A. Johnston, Phys. Rev. E 65, 036105 (2002).
18. M.E.J. Newman, I. Jensen, and R.M. Ziff, Phys. Rev. E 65, 021904 (2002).
19. M. Kuperman and G. Abramson, Phys. Rev. Lett. 86, 2909 (2001).
20. N. Zekri and J.P. Clerc, Phys. Rev. E 64, 056115 (2001).
21. F. Bagnoli and M. Bezzi, Phys. Rev. E 64, 021914 (2001).
22. J. Davidsen, H. Ebel, and S. Bornholdt, Phys. Rev. Lett. 88, 128701 (2002).
23. D.H. Zanette, Phys. Rev. E 65, 041908 (2002).
24. V. Latora and M. Marchiori, Phys. Rev. Lett. 87, 198701 (2001).
25. M.C. Cross and P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
26. P.G. Lind, J. Corte-Real, and J.A.C. Gallas, Phys. Rev. E 66, 016219 (2002).
27. P.G. Lind, J. Corte-Real, and J.A.C. Gallas, Physica D 168-169, 93 (2002).
28. P.G. Lind, S. Titz, T. Kuhlbrodt, J. Corte-Real, J. Kurths, J.A.C. Gallas, and U. Feudel, Int. J. Bifurcation Chaos, Appl. Sci. Eng. (to be published).
29. t(i)-x,(i + 1)| < δ for small 8. Numerically, we used δ=0.001. Although in some situations the above definition was found to lead to spurious results [25], we checked that it is adequate in our case.
30. A. Pikovsky, O. Popovych, and Y. Maistrenko, Phys. Rev. Lett. 87, 044102 (2001).
31. K. Kaneko, Phys. Rev. Lett. 63, 219 (1989); 63, 1029 (1989).
32. K. Kaneko, Phys. Rev. Lett. 63, 219 (1989); 63, 1029 (1989).
33. S.C. Manrubia and A.S. Mikhailov, Phys. Rev. E 60, 1579 (1999).
34. T. Shinbrot, Phys. Rev. E 50, 3230 (1994).
35. M.S. Vieira and A.J. Lichtenberg, Phys. Rev. E 56, R3741 (1997).
36. F.H. Willeboordse, Phys. Rev. E 65, 026202 (2002).
37. P.G. Lind, J.A. Cone-Real, and J.A.C. Gallas, Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, 2647 (2001).
38. H. Chaté and P. Manneville, Chaos 2, 307 (1992).
39. Q. Zhilin, H. Gang, M. Benkun, and T. Gang, Phys. Rev. E 50, 163 (1994).
40. R. Carretero-González, D.K. Arrowsmith, and F. Vivaldi, Phys. Rev. E 61, 1329 (2000).
41. A.M. Baptista and R.L. Viana, Phys. Lett. A 286, 134 (2001).
42. P.G. Lind, J. Cone-Real, and J.A.C. Gallas, Physica A 327, 65 (2003).
43. D.H. Zanette, Phys. Rev. E 55, 5315 (1997).
44. See, e.g., P.J. Davis, Circulant Matrices (Wiley, New York, 1979).
45. G.V. Osipov and J. Kurths, Phys. Rev. E 65, 016216 (2002).