BIFURCATION TO CHAOS IN THE СOMPLEX GINZBURG–LANDAU EQUATION WITH LARGE THIRD-ORDER DISPERSION
https://doi.org/10.18255/1818-1015-2015-3-327-336
Abstract
We give an analytic proof of the existence of Shilnikov chaos in complex Ginzburg– Landau equation subject to a large third-order dispersion perturbation.
About the Authors
I. I. OvsyannikovRussian Federation
D. V. Turaev
United Kingdom
S. V. Zelik
United Kingdom
References
1. Afraimovich V. S., Gonchenko S. V., Lerman L., Shilnikov A., Turaev D., “Scientific heritage of L.P.Shilnikov”, Regul. Chaotic Dyn., 19 (2014), 435–460.
2. Arneodo A., Coullet P. H., Spiegel E. A., Tresser C., “Asymptotic Chaos”, Physica D, 14 (1985), 327–347.
3. Arneodo A., Coullet P. H., Spiegel E. A., “The dynamics of triple convection”, Geophys. Astrophys. Fluid Dyn., 31 (1985), 1–48.
4. Ibanez S., Rodriguez J. A., “Shilnikov configurations in any generic unfolding of the nilpotent singularity of codimension three on R3”, J. Differential Equations, 208 (2005), 147–175.
5. Kostianko A., Titi E., Zelik S., Large dispersion, averaging, and attractors: three 1D paradigms, preprint, 2014.
6. Shilnikov L. P., “A case of the existence of a countable number of periodic motions”, Soviet Math. Dokl., 6 (1965), 163–166.
7. Shilnikov L. P., “A contribution to the problem of the structure of an extended neighbourhood of a rough equilibrium state of saddle-focus type”, Math. USSR-Sb., 10 (1970), 91–102.
8. Turaev D., Zelik S., “Analytical proof of space-time chaos in Ginzburg–Landau Equations”, Discrete Contin. Dyn. Syst., 28 (2010), 1713–1751.
Review
For citations:
Ovsyannikov I.I., Turaev D.V., Zelik S.V. BIFURCATION TO CHAOS IN THE СOMPLEX GINZBURG–LANDAU EQUATION WITH LARGE THIRD-ORDER DISPERSION. Modeling and Analysis of Information Systems. 2015;22(3):327-336. https://doi.org/10.18255/1818-1015-2015-3-327-336