Localized structures as spatial hosts for unstable modesA. Lampert1 and E. Meron1, 2
1 Department of Physics, Ben-Gurion University - Beer-Sheva 84105, Israel
2 Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University - Sede Boqer Campus 84990, Israel
received 5 December 2006; accepted in final form 20 February 2007; published April 2007
published online 23 March 2007
We study spatially extended systems undergoing Hopf-Turing instabilities to temporal oscillations and periodic spatial patterns, focusing on mono-stability regimes where one mode nonlinearly damps the other. Using the pertinent normal-form equations, we identify a new type of instability beyond which localized structures of the dominant mode host the unstable, nonlinearly damped mode. Thus, stationary localized structures of the Turing mode can lose stability to breathing structures that host the Hopf mode, and propagating localized structures of the Hopf mode can lose stability to stationary structures hosting the Turing mode. Hosting instabilities of this kind are expected to be found in other multi-mode systems as well. Potential applications include self-organized waveguides, and data storage.
47.54.-r - Pattern selection; pattern formation.
05.45.-a - Nonlinear dynamics and chaos.
82.40.Bj - Oscillations, chaos, and bifurcations.
© Europhysics Letters Association 2007