Abstract
The phenomenon of time-periodic evolution of spatial chaos is investigated in the frames of one- and two-dimensional complex Ginzburg-Landau equations. It is found that there exists a region of the parameters in which disordered spatial distribution of the field behaves periodically in time; the boundaries of this region are determined. The transition to the regime of spatiotemporal chaos is investigated and the possibility of describing spatial disorder by a system of ordinary differential equations is analyzed. The effect of the size of the system on the shape and period of oscillations is investigated. It is found that in the two-dimensional case the regime of time-periodic spatial disorder arises only in a narrow strip, the critical width of which is estimated. The phenomenon investigated in this paper indicates that a family of limit cycles with finite basins exists in the functional phase space of the complex Ginzburg-Landau equation in finite regions of the parameters.
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References
M. V. Bazhenov, M. I. Rabinovich, and A. L. Fabrikant, InProceedings of the KIT International Workshop on the Physics of Pattern Formation in Complex Dissipative Systems, S. Kai, ed. (World Scientific, Singapore, 1992), p. 361.
Y. Kuramoto,Chemical Oscillations, Waves, and Turbulence, (Springer-Verlag, Berlin, 1984).
A. S. Newell,Lect. Appl. Math. 15:157 (1974).
H. Sakaguchi,Prog. Theor. Phys. 84:792 (1990).
L. Gill,Nonlinearity 4:1213 (1991).
B. I. Shraiman, A. Pumir, W. Saarloos, P. C. Hohenberg, H. Chate, and M. Holen,Physica D 57:241 (1992).
M. V. Bazhenov, M. I. Rabinovich, and A. L. Fabrikant,Phys. Lett. A 163:87 (1992).
H. Chate,Nonlinearity 7:185 (1994).
M. C. Cross and P. C. Hohenberg,Rev. Mod. Phys. 65(3):851 (1993).
K. Nozaki and N. Bekki,J. Phys. Soc. Jpn. 53:1581 (1984).
P. S. Hagan,SIAM J. Appl. Math. 42:762 (1982).
I. Aranson, L. Kramer, S. Popp, O. Stiller, and A. Weber,Phys. Rev. Lett. 70:3880 (1993).
A. Weber, L. Kramer, I. S. Aranson, and L. Aranson,Phys. Rev. A 46:R2992 (1992).
H. Sakaguchi,Prog. Theor. Phys. 85:417 (1991).
I. Arnson, L. Kramer, and A. Weber,Phys. Rev. Lett. 72:2316 (1994).
S. A. Orszag,Stud. Appl. Math. 20:293 (1971). C. Canuto, M. J. Hussaini, A. Quarteroni, and T. A. Zand,Spectral Methods in Fluid Dynamics (Springer, Berlin, 1988).
A. M. Fraser and H. L. Swinney,Phys. Rev. A 33:1134 (1986).
M. Bazhenov and M. Rabinovich,Physica D 73:318 (1994).
F. H. Willeboordse and K. Kaneko,Phys. Rev. Lett. 73:533 (1994).
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Bazhenov, M., Rabinovich, M. & Rubchinsky, L. Time-periodic spatial chaos in the complex Ginzburg-Landau equation. J Stat Phys 83, 1165–1181 (1996). https://doi.org/10.1007/BF02179556
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DOI: https://doi.org/10.1007/BF02179556