Competing resonances in spatially forced pattern-forming systems

Yair Mau*, Lev Haim, Aric Hagberg, Ehud Meron

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Spatial periodic forcing can entrain a pattern-forming system in the same way as temporal periodic forcing can entrain an oscillator. The forcing can lock the pattern's wave number to a fraction of the forcing wave number within tonguelike domains in the forcing parameter plane, it can increase the pattern's amplitude, and it can also create patterns below their onset. We derive these results using a multiple-scale analysis of a spatially forced Swift-Hohenberg equation in one spatial dimension. In two spatial dimensions the one-dimensional forcing can induce a symmetry-breaking instability that leads to two-dimensional (2D) patterns, rectangular or oblique. These patterns resonate with the forcing by locking their wave-vector component in the forcing direction to half the forcing wave number. The range of this type of 2:1 resonance overlaps with the 1:1 resonance tongue of stripe patterns. Using a multiple-scale analysis in the overlap region we show that the 2D patterns can destabilize the 1:1 resonant stripes even at exact resonance. This result sheds new light on the use of spatial periodic forcing for controlling patterns.

Original languageAmerican English
Article number032917
JournalPhysical Review E
Issue number3
StatePublished - 25 Sep 2013
Externally publishedYes


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