Instabilities and tracking of travelling wave patterns in a three-level laser

Based on our earlier theoretical work on tracking periodic patterns into sp atiotemporal chaotic regimes in spatially extended systems, we present in t his article a case study of a high-aspect-ratio three-level laser. Followin g a detailed investigation into travelling wave solutions of the laser syst em and their stability conditions, we discuss ways of stabilising these sol utions by local feedback algorithms. In numerical simulations, we choose Py ragus continuous delayed feedback algorithm to be the local feedback form a nd demonstrate that stable travelling wave solutions of the spatially exten ded three-level laser can be greatly extended to unstable regions in the pr esence of this feedback.