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

Table 1

The values of 𝑔₀ associated with each bifurcation in the ODE and PDE. The labels correspond to the bifurcations of the ODE in Figure 13. Values in parenthesis are estimated from the same figure.

Label	Bifurcation type	ODE	Even PDE
(a)	Saddle node	0.7229	0.6522
(b)	Saddle node	1.424	1.429
(c)	Hopf	1.398	1.369
(d)	Hopf	1.753	2.404
(e)	Period doubling	3.3872	(3.0±0.1)
(f)	Neimark-Sacker	3.3873	(3.0±0.1)