The transition from phase chaos to defect chaos in the complex
Ginzburg-Landau equation (CGLE) is related to saddle-node bifurcations of
modulated amplitude waves (MAWs). First, the spatial period P of MAWs is shown
to be limited by a maximum P_SN which depends on the CGLE coefficients;
MAW-like structures with period larger than P_SN evolve to defects. Second,
slowly evolving near-MAWs with average phase gradients ν≈0 and
various periods occur naturally in phase chaotic states of the CGLE. As a
measure for these periods, we study the distributions of spacings p between
neighboring peaks of the phase gradient. A systematic comparison of p and P_SN
as a function of coefficients of the CGLE shows that defects are generated at
locations where p becomes larger than P_SN. In other words, MAWs with period
P_SN represent ``critical nuclei'' for the formation of defects in phase chaos
and may trigger the transition to defect chaos. Since rare events where p
becomes sufficiently large to lead to defect formation may only occur after a
long transient, the coefficients where the transition to defect chaos seems to
occur depend on system size and integration time. We conjecture that in the
regime where the maximum period P_SN has diverged, phase chaos persists in the
thermodynamic limit.Comment: 25 pages, 18 figure
