Hexagon Invasion Fronts Outside the Homoclinic Snaking Region in the Planar Swift-Hohenberg Equation

  title={Hexagon Invasion Fronts Outside the Homoclinic Snaking Region in the Planar Swift-Hohenberg Equation},
  author={David J. B. Lloyd},
  journal={SIAM J. Appl. Dyn. Syst.},
  • D. Lloyd
  • Published 10 November 2019
  • Mathematics
  • SIAM J. Appl. Dyn. Syst.
Stationary fronts connecting the trivial state and a cellular (distorted) hexagonal pattern in the Swift-Hohenberg equation are known to undergo a process of infinitely many folds as a parameter is varied, known as homoclinic snaking, where new hexagon cells are added to the core, leading to the co-existence of infinitely-many localised states in the bistable region. Outside the homoclinic snaking region, the hexagon fronts can invade the trivial state in a bursting fashion. In this paper, we… 



Invasion Fronts Outside the Homoclinic Snaking Region in the Planar Swift-Hohenberg Equation

  • D. Lloyd
  • Mathematics
    SIAM J. Appl. Dyn. Syst.
  • 2019
In this paper, we carry out numerical bifurcation analysis of depinning of fronts near the homoclinic snaking region, involving a spatial stripe cellular pattern embedded in a quiescent state, in the

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