Modulational instability and spatiotemporal transition to chaos

The one-dimensional generalized modified complex Ginzburg–Landau equation [Malomed BA, Stenflo L. J Phys A: Math Gen 1991;24:L1149] is considered. The linear stability analysis is used in order to derive the conditions for modulational instability. We obtained the generalized Lange and Newell’s criterion for modulational instability. Numerical simulation shows the validity of the analytical approach. The model presents a rich variety of patterns propagating in the system and a spatiotemporal transition to chaos.