Two-dimensional localized structures in harmonically forced oscillatory systems

Ma, Yi-Ping and Knobloch, Edgar (2016) Two-dimensional localized structures in harmonically forced oscillatory systems. Physica D: Nonlinear Phenomena, 337. pp. 1-17. ISSN 0167-2789

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Official URL: http://dx.doi.org/10.1016/j.physd.2016.07.003

Abstract

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.

Item Type: Article
Uncontrolled Keywords: Oscillons; Localized patterns; Forced complex Ginzburg–Landau equation; Snaking
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Yi-Ping Ma
Date Deposited: 10 Nov 2016 08:29
Last Modified: 07 Sep 2017 03:46
URI: http://nrl.northumbria.ac.uk/id/eprint/28402

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