Proximity to periodic windows in bifurcation diagrams as a gateway to coherence resonance in chaotic systems

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

Volumn 76, Issue 3, 2007, Pages

  Gosak, Marko ^a   Perc, Matjaž ^a  

^a UNIVERSITY OF MARIBOR   (Slovenia)

Author keywords

[No Author keywords available]

Indexed keywords

ADDITIVE NOISE; CHAOTIC SYSTEMS; GAUSSIAN NOISE (ELECTRONIC); LORENTZ FORCE; WAVELET ANALYSIS;

CHAOTIC STATES; COHERENCE RESONANCE; LORENZ EQUATIONS;

PERIODIC STRUCTURES;

EID: 34748844676     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.037201     Document Type: Article

References (48)

1. W. Horsthemke and R. Lefever, Noise-Induced Transitions (Springer-Verlag, Berlin, 1984);
2. P. Hänggi and R. Bartussek, in Nonlinear Physics of Complex Systems, edited by, J. Parisi, S. C. Müller, and, W. Zimmermman, (Springer, New York, 1999).
3. R. Benzi, A. Sutera, and A. Vulpiani, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/14/11/006 14, L453 (1981);
4. C. Nicolis and G. Nicolis, Tellus TELLAL 0040-2826 33, 225 (1981);
5. Examples of reviews are P. Jung, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(93)90022-6 234, 175 (1993);
6. F. Moss, A. Bulsara, and M. F. Shlesinger, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01053949 70, 1 (1993);
7. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.70.223 70, 223 (1998).
8. A. S. Pikovsky and J. Kurths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.775 78, 775 (1997).
9. D. Sigeti and W. Horsthemke, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01044713 54, 1217 (1989);
10. Hu Gang, T. Ditzinger, C. Z. Ning, and H. Haken, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.807 71, 807 (1993);
11. W. J. Rappel and S. H. Strogatz, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.50.3249 50, 3249 (1994).
12. J. R. Pradines, G. V. Osipov, and J. J. Collins, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.6407 60, 6407 (1999);
13. For a review, see B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geier, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2003.10.015 392, 321 (2004).
14. A. Neiman, P. I. Saparin, and L. Stone, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.56.270 56, 270 (1997);
15. Z. Hou and H. Xin, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.6329 60, 6329 (1999);
16. A. Rozenfeld, C. J. Tessone, E. Albano, and H. S. Wio, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(01)00033-0 280, 45 (2001);
17. S. Katsev and I. L'Heureux, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.4972 61, 4972 (2000);
18. M. Perc and M. Marhl, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71. 026229 71, 026229 (2005);
19. O. V. Ushakov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95. 123903 95, 123903 (2005).
20. A. Pikovsky, A. Zaikin, and M. A. de la Casa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.050601 88, 050601 (2002);
21. R. Toral, C. R. Mirasso, and J. D. Gunton, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-00207-5 61, 162 (2003);
22. M. Wang, Z. Hou, and H. Xin, ChemPhysChem CPCHFT 1439-4235 10.1002/cphc.200400255 5, 1602 (2004).
23. C. J. Tessone, C. R. Mirasso, R. Toral, and J. D. Gunton, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.194101 97, 194101 (2006).
24. J. García-Ojalvo and J. M. Sancho, Noise in Spatially Extended Systems (Springer, New York, 1999).
25. H. Busch and F. Kaiser, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.041105 67, 041105 (2003);
26. E. Ullner, A. A. Zaikin, J. García-Ojalvo, and J. Kurths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.180601 91, 180601 (2003);
27. O. Carrillo, M. A. Santos, J. García-Ojalvo, and J. M. Sancho, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-10105-4 65, 452 (2004);
28. C. S. Zhou and J. Kurths, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/018 7, 18 (2005);
29. M. Perc and M. Marhl, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73. 066205 73, 066205 (2006);
30. E. Glatt, H. Busch, F. Kaiser, and A. Zaikin, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.026216 73, 026216 (2006);
31. Q. Y. Wang, Q. S. Lu, and G. R. Chen, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/77/10004 77, 10004 (2007).
32. H. Herzel and B. Pompe, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(87)90788-2 122, 121 (1987);
33. F. Gassmann, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.2215 55, 2215 (1997).
34. A. Maritan and J. R. Banavar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.1451 72, 1451 (1994);
35. H. Herzel and J. Freund, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.52.3238 52, 3238 (1995).
36. G. Nicolis, C. Nicolis, and D. McKernan, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01053958 70, 125 (1993);
37. A. Crisanati, M. Falcioni, G. Paladin, and A. Vulpiani, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/27/17/001 27, L597 (1994).
38. C. Palenzuela, R. Toral, C. R. Mirasso, O. Calvo, and J. D. Gunton, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2001-00526-5 56, 347 (2001).
39. Z. Liu and Y.-C. Lai, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.4737 86, 4737 (2001).
40. Y.-C. Lai and Z. Liu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64. 066202 64, 066202 (2001).
41. M. Zhan, G. W. Wei, C.-H. Lai, Y.-C. Lai, and Z. Liu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.036201 66, 036201 (2002).
42. J. B. Gao, S. K. Hwang, and J. M. Liu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.1132 82, 1132 (1999);
43. J. B. Gao, W. W. Tung, and N. Rao, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.254101 89, 254101 (2002).
44. S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, MA, 1994).
45. G. Kaiser, A Friendly Guide to Wavelets (Birkhauser, Boston, 1994).
46. I. Daubechies, Commun. Pure Appl. Math. CPMAMV 0010-3640 41, 906 (1988).
47. F. Chapeau-Blondeau and D. Rousseau, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127405013824 15, 2985 (2005);
48. F. Chapeau-Blondeau, S. Blanchard, and D. Rousseau, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.74.031102 74, 031102 (2006).