The Proper Orthogonal Decomposition for Dimensionality Reduction in Mode-Locked Lasers and Optical Systems

Figure 13

Top: the bifurcation diagram of energy (𝐿² norm) versus 𝑔₀ for the multi-pulse transition in the POD model. Bottom: the bifurcation diagram of the multi-pulse transition of the WGAML model. The different plots show the same diagram with emphasis on different regions of the transition. For the stationary solutions, emphasized on the left, linearly unstable regions are dashed (red) lines while linearly stable regions are solid (blue) lines. Stationary solutions that were not computed explicitly are denoted with dots. For the periodic solutions, the 𝑥s are the local extrema of the energy (𝐿² norm).