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

Based on our earlier theoretical work on tracking periodic patterns into spatiotemporal chaotic regimes in spatially extended systems, we present in this article a case study of a high-aspect-ratio three-level laser. Following a detailed investigation into travelling wave solutions of the laser system and their stability conditions, we discuss ways of stabilising these solutions by local feedback algorithms. In numerical simulations, we choose Pyragus continuous delayed feedback algorithm to be the local feedback form and demonstrate that stable travelling wave solutions of the spatially extended three-level laser can be greatly extended to unstable regions in the presence of this feedback.