Issue
EPL
Volume 83, Number 1, July 2008
Article Number 10005
Number of page(s) 5
Section General
DOI http://dx.doi.org/10.1209/0295-5075/83/10005
Published online 16 June 2008
EPL, 83 (2008) 10005
DOI: 10.1209/0295-5075/83/10005

Wave-number locking in spatially forced pattern-forming systems

R. Manor1, A. Hagberg2 and E. Meron1, 3

1  Physics Department, Ben-Gurion University - Beer-Sheva 84105, Israel
2  Mathematical Modeling and Analysis, Theoretical Division, Los Alamos National Laboratory Los Alamos, NM 87545, USA
3  Department of Solar Energy and Environmental Physics, BIDR, Ben Gurion University Sede Boker Campus 84990, Israel

hagberg@lanl.gov

received 28 February 2008; accepted in final form 19 May 2008; published July 2008
published online 16 June 2008

Abstract
We use the Swift-Hohenberg model and normal-form equations to study wave-number locking in two-dimensional systems as a result of one-dimensional spatially periodic weak forcing. The freedom of the system to respond in a direction transverse to the forcing leads to wave-number locking in a wide range of forcing wave-numbers, even for weak forcing, unlike the locking in a set of narrow Arnold tongues in one-dimensional systems. Multi-stability ranges of stripe, rectangular, and oblique patterns produce a variety of resonant patterns. The results shed new light on rehabilitation practices of banded vegetation in drylands.

PACS
05.45.-a - Nonlinear dynamics and chaos.
05.45.Xt - Synchronization; coupled oscillators.
47.54.-r - Pattern selection; pattern formation.

© EPLA 2008