Additive Temporal Coloured Noise Induced Eckhaus Instability in Complex Ginzburg--Landau Equation System

The effect of additive coloured noises, which are correlated in time, on one-dimensional travelling waves in the complex Ginzburg--Landau equation is studied by numerical simulations. We found that a small coloured noise with temporal correlation could considerably influence the stability of one-dimensional wave trains. There exists an optimal temporal correlation of noise where travelling waves are the most vulnerable. To elucidate the phenomena, we statistically calculated the convective velocities V_g of the wave packets, and found that the coloured noise with an appropriate temporal correlation can decrease V_g, making the system convectively more unstable.