THEME SECTION: New Trends in the Applications of Dynamical System Theory — PapersNo Access

SYNCHRONIZATION OF CHAOS AND THE TRANSITION TO WAVE TURBULENCE

R. L. VIANA

Department of Physics, Federal University of Paraná, 81531-990 Curitiba, Paraná, Brazil

Search for more papers by this author

S. R. LOPES

Department of Physics, Federal University of Paraná, 81531-990 Curitiba, Paraná, Brazil

Search for more papers by this author

J. D. SZEZECH, JR.

Institute of Physics, University of São Paulo, 05315-970 São Paulo, São Paulo, Brazil

Search for more papers by this author

, and

I. L. CALDAS

Institute of Physics, University of São Paulo, 05315-970 São Paulo, São Paulo, Brazil

Search for more papers by this author

https://doi.org/10.1142/S0218127412502343Cited by:1 (Source: Crossref)

Abstract

We investigated the transition to wave turbulence in a spatially extended three-wave interacting model, where a spatially homogeneous state undergoing chaotic dynamics undergoes spatial mode excitation. The transition to this weakly turbulent state can be regarded as the loss of synchronization of chaos of mode oscillators describing the spatial dynamics.

Keywords:

References

V. S. Afraimovich, N. N. Verichev and M. I. Rabinovich, Radiophys. Quant. Electron. 29, 795 (1986), DOI: 10.1007/BF01034476. Crossref, Google Scholar
A. C.-L. Chian, S. R. Lopes and M. V. Alves, Astron. Astrophys. 290, L13 (1994). Web of Science, Google Scholar
A. C.-L. Chian and F. B. Rizzato, J. Plas. Phys. 51, 61 (1994), DOI: 10.1017/S0022377800017396. Crossref, Web of Science, Google Scholar
C. C. Chow, A. Bers and A. K. Ram, Phys. Rev. Lett. 68, 3379 (1992), DOI: 10.1103/PhysRevLett.68.3379. Crossref, Web of Science, Google Scholar
S. Dyachenkoet al., Physica D 57, 96 (1992), DOI: 10.1016/0167-2789(92)90090-A. Crossref, Web of Science, Google Scholar
U. Frisch , Turbulence: The Legacy of A. N. Kolmogorov ( Cambridge University Press , Cambridge , 1995 ) . Crossref, Google Scholar
H. Fujisaka and T. Yamada, Prog. Theor. Phys. 69, 32 (1983), DOI: 10.1143/PTP.69.32. Crossref, Web of Science, Google Scholar
A. C. Hindmarch , Scientific Computing , eds. R. S. Stepleman et al. ( North-Holland , Amsterdam , 1983 ) . Google Scholar
D. J. Kaup, A. Reiman and A. Bers, Rev. Mod. Phys. 51, 275 (1979), DOI: 10.1103/RevModPhys.51.275. Crossref, Web of Science, Google Scholar
G. V. Kolmakov and V. L. Pokrovsky, Physica D 86, 465 (1995). Google Scholar
Y. Kuramoto , Chemical Oscillations, Waves, and Turbulence ( Springer-Verlag , Berlin , 1984 ) . Crossref, Google Scholar
L. D. Landau and E. M. Lifshitz , Fluid Mechanics , 2nd edn. ( Pergamon Press , NY , 1987 ) . Crossref, Google Scholar
S. R. Lopes and A. C.-L. Chian, Phys. Rev. E 54, 170 (1996), DOI: 10.1103/PhysRevE.54.170. Crossref, Web of Science, Google Scholar
S. R. Lopes and F. B. Rizzato, Phys. Rev. E 60, 5375 (1999), DOI: 10.1103/PhysRevE.60.5375. Crossref, Web of Science, Google Scholar
Y. C. Li, Int. J. Bifurcation and Chaos 17, 85 (2007). Link, Web of Science, Google Scholar
S. L. Musher, A. M. Rubenchik and V. E. Zakharov, Phys. Rep. 252, 177 (1995), DOI: 10.1016/0370-1573(94)00071-A. Crossref, Google Scholar
S. Newhouse, D. Ruelle and F. Takens, Comm. Math. Phys. 64, 35 (1978), DOI: 10.1007/BF01940759. Crossref, Web of Science, Google Scholar
G. V. Osipovet al., Phys. Rev. Lett. 91, 024101 (2003), DOI: 10.1103/PhysRevLett.91.024101. Crossref, Web of Science, Google Scholar
L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990), DOI: 10.1103/PhysRevLett.64.821. Crossref, Web of Science, Google Scholar
A. Picozzi and M. Haeltermann, Phys. Rev. Lett. 86, 2010 (2001), DOI: 10.1103/PhysRevLett.86.2010. Crossref, Web of Science, Google Scholar
A. S. Pikovsky , M. G. Rosenblum and J. Kurths , Synchronization: A Universal Concept in Nonlinear Sciences ( Springer-Verlag , NY-Berlin-Heidelberg , 2001 ) . Crossref, Google Scholar
D. Ruelle and F. Takens, Commun. Math. Phys. 20, 167 (1971), DOI: 10.1007/BF01646553. Crossref, Web of Science, Google Scholar
A. Rundquistet al., Science 280, 1412 (1998), DOI: 10.1126/science.280.5368.1412. Crossref, Web of Science, Google Scholar
E. Schröderet al., Phys. Rev. Lett. 76, 4717 (1996). Crossref, Web of Science, Google Scholar
S. Sridhar and P. Goldreich, Astrophys. J. 432, 612 (1994), DOI: 10.1086/174600. Crossref, Web of Science, Google Scholar
G. I. Stegeman and M. Segev, Science 286, 1518 (1999), DOI: 10.1126/science.286.5444.1518. Crossref, Web of Science, Google Scholar
J. D. Szezech Jr., S. R. Lopes and R. L. Viana, Phys. Rev. E 75, 067202-1 (2007), DOI: 10.1103/PhysRevE.75.067202. Web of Science, Google Scholar
J. D. Szezech Jr.et al., Physica D 238, 516 (2009), DOI: 10.1016/j.physd.2008.11.015. Crossref, Web of Science, Google Scholar
J. D. Szezech Jr.et al., Physica A 390, 365 (2011), DOI: 10.1016/j.physa.2010.09.037. Crossref, Web of Science, Google Scholar
L. Turner, Phys. Rev. E 54, 5822 (1996), DOI: 10.1103/PhysRevE.54.5822. Crossref, Web of Science, Google Scholar
A. Wolfet al., Physica D 16, 285 (1985), DOI: 10.1016/0167-2789(85)90011-9. Crossref, Web of Science, Google Scholar
M. Yamada and K. Ohkitani, Phys. Rev. Lett. 60, 983 (1988), DOI: 10.1103/PhysRevLett.60.983. Crossref, Web of Science, Google Scholar
Zakharov, V. E. & Sagdeev, R. Z. [1970] "Spectrum of acoustic turbulence," Sov. Phys. Dokl. 15, 439–441; Russian original: Dokl. Akad. Nauk. SSSR 192, 297–300 . Google Scholar
V. E. Zakharov, F. Dias and A. Pushkarev, Phys. Rep. 398, 1 (2004), DOI: 10.1016/j.physrep.2004.04.002. Crossref, Web of Science, Google Scholar