Modulated amplitude waves and the transition from phase to defect chaos
The mechanism for transitions from phase to defect chaos in the one-dimensional complex Ginzburg-Landau equation (CGLE) is presented. We describe periodic coherent structures of the CGLE, called modulated amplitude waves (MAWs). MAWs of various periods P occur in phase chaotic states. A bifurcation study of the MAWs reveals that for sufficiently large period, pairs of MAWs cease to exist via a saddle-node bifurcation. For periods beyond this bifurcation, incoherent near-MAW structures evolve towards defects. This leads to our main result: the transition from phase to defect chaos takes place when the periods of MAWs in phase chaos are driven beyond their saddle-node bifurcation.
Brusch
L
Max-Planck-Institut fur Physik komplexer Systeme, Nothnitzer Strasse 38, D-01187 Dresden, Germany.
Zimmermann
MG
van Hecke M
Bar
M
Torcini
A