A discrete and periodic complex Ginzburg-Landau equation, coupled to a mean is systematically derived from driven dissipative lattice oscillator model, close the onset of supercritical Andronov-Hopf bifurcation. The model inspired by recent experiments exploring active vibrations quasi-one-dimensional lattices self-propelled millimetric droplets bouncing on vertically vibrating fluid bath. Our ...

Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered. For parameters close to the vortex limit, and for a system of spiral waves with well-separated centres, laws of motion of the centres are found which vary depending on the order of magnitude of the separation of the centres. In particular, the direction of the interaction changes fro...

We study the set of solutions of the complex Ginzburg-Landau equation in R, d < 3. We consider the global attracting set (i.e., the forward map of the set of bounded initial data), and restrict it to a cube Q L of side L. We cover this set by a (minimal) number N QL (ε) of balls of radius ε in L∞(Q L ). We show that the Kolmogorov ε-entropy per unit length, H ε = lim L→∞ L −d log N QL (ε) exist...

Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered, and laws of motion for the centers are derived. The direction of the motion changes from along the line of centers to perpendicular to the line of centers as the separation increases, with the strength of the interaction algebraic at small separations and exponentially small at large...

It is shown that the complex Ginzburg-Landau (CGL) equation on the real line admits nontrivial 2-periodic vortex solutions that have 2n simple zeros (\vortices") per period. The vortex solutions bifurcate from the trivial solution and inherit their zeros from the solution of the linearized equation. This result rules out the possibility that the vortices are determining nodes for vortex solutio...

We study patterns that arise in the wake of an externally triggered, spatially propagating instability in the complex Ginzburg-Landau equation. We model the trigger by a spatial inhomogeneity moving with constant speed. In the comoving frame, the trivial state is unstable to the left of the trigger and stable to the right. At the trigger location, spatio-temporally periodic wavetrains nucleate....