Fluctuations and pattern selection near an Eckhaus instability

Fluctuations and pattern selection near an Eckhaus instability.

X iv :c on dm at /9 30 20 28 v1 1 9 Fe b 19 93 Fluctuations and pattern selection near an Eckhaus instability E. Hernández-Garćıa, Jorge Viñals, Raúl Toral, and M. San Miguel 1Departament de F́ısica, Universitat de les Illes Balears E-07071 Palma de Mallorca, Spain 2Supercomputer Computations Research Institute, B-186 Florida State University, Tallahassee, Florida 32306-4052 3Institut d’Estudis ...

Pattern selection near the onset of convection: The Eckhaus instability.

Eckhaus instability and homoclinic snaking.

Homoclinic snaking is a term used to describe the back and forth oscillation of a branch of time-independent spatially localized states in a bistable, spatially reversible system as the localized structure grows in length by repeatedly adding rolls on either side. This behavior is simplest to understand within the subcritical Swift-Hohenberg equation, but is also present in the subcritical regi...

Phase Slips and the Eckhaus Instability

We consider the Ginzburg-Landau equation, @ t u = @ 2 x u+u?ujuj 2 , with complex amplitude u(x; t). We first analyze the phenomenon of phase slips as a consequence of the local shape of u. We next prove a global theorem about evolution from an Eckhaus unstable state, all the way to the limiting stable finite state, for periodic perturbations of Eckhaus unstable periodic initial data. Equipped ...

Critical Fluctuations in Cortical Models Near Instability

Computational studies often proceed from the premise that cortical dynamics operate in a linearly stable domain, where fluctuations dissipate quickly and show only short memory. Studies of human electroencephalography (EEG), however, have shown significant autocorrelation at time lags on the scale of minutes, indicating the need to consider regimes where non-linearities influence the dynamics. ...