Instabilities of the Ginzburg-Landau equation. II. Secondary bifurcation
Authors:
Paul K. Newton and Lawrence Sirovich
Journal:
Quart. Appl. Math. 44 (1986), 367-374
MSC:
Primary 35Q20; Secondary 58E07
DOI:
https://doi.org/10.1090/qam/856192
MathSciNet review:
856192
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Abstract: A perturbation treatment of secondary bifurcation for the Ginzburg-Landau equation is presented. An analytical form for limit cycle instability is determined. This is compared with numerical results and shown to be in good agreement over a wide parameter range.
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H. T. Moon, P. Huerre and L. G. Redekopp, Three frequency motion and chaos in the Ginzburg-Landau equation, Phys. Rev. Letters 49, #7 (16 Aug. 1984)
H. T. Moon, P. Huerre, and L. G. Redekopp, Transitions to chaos in the Ginzburg-Landau equation, Physica 7D, 135 (1983)
K. Nozaki and N. Bekki, Pattern selection and spatio-temporal transition to chaos in the Ginzburg-Landau equation, Phys., Rev. Letters 51, #29 (12 Dec. 1983)
Y. Kuramoto, Diffusion induced chaos in reaction systems, Supp. Prog. Theor. Phys., No. 64 (1978)
C. S. Bretherton and E. A. Spiegel, Intermittency through modulational instability, Physics Letters 96A, #3 (20 June 1983)
L. Keefe, Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation, Studies in Applied Math. 73, 91 (1985)
R. J. Deissler, Noise-sustained structure, intermittency and the Ginzburg-Landau equation, submitted for publication
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L. Sirovich, P. K. Newton, Periodic solutions of the Ginzburg-Landau equation, to appear, Physica 19D (1986)
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Article copyright:
© Copyright 1986
American Mathematical Society
