Two-dimensional localized structures in harmonically forced oscillatory systems

PHYSICA D-NONLINEAR PHENOMENA

卷:337

Article

Ma, Y. -P.¹  Knobloch, E.² 

[1] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

[2] Univ Calif Berkeley, Dept Phys, Berkeley, CA 94720 USA

关键词: Oscillons;    Localized patterns;    Forced complex Ginzburg-Landau equation;    Snaking;   

DOI  :  10.1016/j.physd.2016.07.003

来源: Elsevier

【 摘 要 】

Two-dimensional spatially localized structures in the complex Ginzburg-Landau equation with 1:1 resonance are studied near the simultaneous presence of a steady front between two spatially homogeneous equilibria and a supercritical Turing bifurcation on one of them. The bifurcation structures of steady circular fronts and localized target patterns are computed in the Turing-stable and Turing unstable regimes. In particular, localized target patterns grow along the solution branch via ring insertion at the core in a process reminiscent of defect-mediated snaking in one spatial dimension. Stability of axisymmetric solutions on these branches with respect to axisymmetric and nonaxisymmetric perturbations is determined, and parameter regimes with stable axisymmetric oscillons are identified. Direct numerical simulations reveal novel depinning dynamics of localized target patterns in the radial direction, and of circular and planar localized hexagonal patterns in the fully two-dimensional system. Published by Elsevier B.V.

【 授权许可】

Free