We show that in a parameter range which is important in particular for optical instabilities spiral waves in the complex (generalized) Ginzburg-Landau equation are unstable with respect to a core instability which leads to spontaneous acceleration of the spiral. Depending on the parameters the system settles down in at least four qualitatively different spatiotemporally chaotic states.

• Received 3 September 1993

DOI:https://doi.org/10.1103/PhysRevLett.72.2316