Spatiotemporal chaos induced by a multiplicative noise process

It is shown that the complex, time-dependent Ginzburg-Landau equation exhibits chaotic behavior under external multiplicative noise. Conditions which bring about the chaos for the system without spatial degrees of freedom are elucidated. Near the transition point from the steady state to the chaos, intermittent time evolution is found, and the power spectrum displays a power law. Inclusion of spatial degrees of freedom leads to the spatiotemporal chaos, and the spatiotemporal power spectra satisfy the dynamical scaling law.