• Media type: E-Article
  • Title: Pattern formation in forced reaction diffusion systems with nearly degenerate bifurcations
  • Contributor: Halloy, José; Sonnino, Giorgio; Coullet, Pierre
  • imprint: AIP Publishing, 2007
  • Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science
  • Language: English
  • DOI: 10.1063/1.2776127
  • ISSN: 1089-7682; 1054-1500
  • Keywords: Applied Mathematics ; General Physics and Astronomy ; Mathematical Physics ; Statistical and Nonlinear Physics
  • Origination:
  • Footnote:
  • Description: <jats:p>The existence and stability of stable standing-wave patterns in an assembly of spatially distributed generic oscillators governed by a couple of complex Ginzburg-Landau equations, subjected to parametric forcing, are reported. The mechanism of a dispersion-induced pattern in dissipative oscillators parametrically forced near the degenerate Turing-Hopf bifurcation is also illustrated. We show that, when excitation occurs just after the Turing bifurcation and before the Hopf instability, the system exhibits a new type of stable standing-wave structures, namely the mixed-mode solutions. The Brussellator-model, parametrically forced below the threshold of oscillations, is analyzed as an example of calculation.</jats:p>