Bounded solutions of nonlocal complex ginzburg-Landau equations for a subcritical bifurcation

Vladimir Volpert, A. A. Nepomnnyashchy, L. G. Stanton, A. A. Golovin

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Stable periodic solutions of a system of two nonlocal coupled complex Ginzburg-Landau (CGL) equations describing the dynamics of a subcritical Hopf bifurcation in a spatially extended system are found analytically in the limit of large dispersion coefficients. The domains in the parameter space where these solutions exist and are stable are determined. It is shown that the existence and stability depend on the sign of the coupling parameter and on the ratio of the dispersion coefficients. Numerical simulations of the system of nonlocal coupled CGL equations confirm the analytical results and exhibit other bounded dynamic regimes, such as standing waves and spatio-temporal chaos.

Original languageEnglish (US)
Pages (from-to)265-283
Number of pages19
JournalSIAM Journal on Applied Dynamical Systems
Volume7
Issue number2
DOIs
StatePublished - Dec 11 2008

Keywords

  • Complex ginzburg-landan equation
  • Hopf bifurcation
  • Nonlocal equations
  • Subcritical instability

ASJC Scopus subject areas

  • Analysis
  • Modeling and Simulation

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