Complex Ginzburg-Landau equation with nonlocal coupling

Title Complex Ginzburg-Landau equation with nonlocal coupling

Nonlocal complex Ginzburg-Landau equation for electrochemical systems.

By means of an extended center-manifold reduction, we derive the nonlocal complex Ginzburg-Landau equation (NCGLE) valid for electrochemical systems with migration coupling. We carry out the stability analysis of the uniform oscillation, elucidating the role of the nonlocal coupling in electrochemical systems at the vicinity of a supercritical Hopf bifurcation. We apply the NCGLE to an experime...

The Complex Ginzburg-landau Equation∗

Essential to the derivation of the Ginzburg-Landau equation is assumption that the spatial variables of the vector field U(x, y, t) are defined on a cylindrical domain. This means that (x, y) ∈ R ×Ω, where Ω ⊂ R is a open and bounded domain (and m ≥ 1, n ≥ 0), so that U : R ×Ω×R+ → R . The N ×N constant coefficient matrix Sμ is assumed to be non-negative, in the sense that all its eigenvalues a...

On a Cubic-quintic Ginzburg-landau Equation with Global Coupling

We study standing wave solutions in a parabolic partial diierential equations which consists of a cubic-quintic equation stabilized by global coupling A 2 (y) dy : We classify the existence and stability of all posssible standing wave solutions.

The Complex Ginzburg-Landau equation for beginners

Several systems discussed at this workshop on Spatio-Temporal Patterns in Nonequilibrium Complex Systems have been related to or analyzed in the context of the so-called Complex Ginzburg-Landau equation (CGL). What is the difference between the physics underlying the usual amplitude description for stationary patterns and the one underlying the CGL? Why are there many more stable coherent struc...