Ginzburg-Landau amplitude equation for nonlinear nonlocal models

Nonlocal Ginzburg-Landau equation for cortical pattern formation.

We show how a nonlocal version of the real Ginzburg-Landau (GL) equation arises in a large-scale recurrent network model of primary visual cortex. We treat cortex as a continuous two-dimensional sheet of cells that signal both the position and orientation of a local visual stimulus. The recurrent circuitry is decomposed into a local part, which contributes primarily to the orientation tuning pr...

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...

Weakly Nonlocal Irreversible Thermodynamics- the Ginzburg-landau Equation

The variational approach to weakly nonlocal thermodynamic theories is critically revisited in the light of modern nonequilibrium thermody-namics. The example of Ginzburg-Landau equation is investigated in detail.

Title Complex Ginzburg-Landau equation with nonlocal coupling

Model Reduction of the Nonlinear Complex Ginzburg-Landau Equation

Reduced-order models of the nonlinear Complex Ginzburg-Landau (CGL) equation are computed using a nonlinear generalization of balanced truncation. The method involves Galerkin projection of the nonlinear dynamics onto modes determined by balanced truncation of a linearized system, and is compared to a standard method using projection onto Proper Orthogonal Decomposition (POD) modes computed fro...