The universality of the Stuart-Landau equation to describe nonlinear oscillators I have read numerous papers which boldly suggest that the Stuart-Landau equation can be successfully used to model any weakly nonlinear oscillating system near a Hopf bifurcation. Even thought it has been touted as one of the most celebrated equations in nonlinear science, I am having a hard time understanding what fundamentally allows this equation to be applied to such a wide array of systems. Is there a natural law which massages most oscillating systems to behave this way? 
Does anyone know where this equation has successfully been used to model a natural system? Any elucidation would be greatly appreciated. I'm looking for justification to use this as a basis for a phenomenological model for a system of my own interest.
 A: Short explanation: Physical systems are usually dissipative systems. Dissipative systems can be modelled with a 1st order ODE system. If you do your perturbation analysis on this system at the Hopf bifurcation and take higher orders into account, you end up with the Stuart-Landau equation. 
Hence by derivation, it describes the dynamics of a system infinitesimally close at the Hopf bifurcation.
One application: Oscillating chemical reactions like the Belousov-Zhabotinsky reaction.
Source: famous book by Kuramoto (1984): Chemical Oscillations and waves.
A: I'm finding it very useful to model brain oscillations.
Here I use 90 SL oscillators coupled together with time delays in the structural network of the brain and report the emergent behaviour
Synchronization in the connectome: Metastable oscillatory modes emerge from interactions in the brain spacetime network
Joana Cabral, Francesca Castaldo, Jakub Vohryzek, Vladimir Litvak, Christian Bick, Renaud Lambiotte, Karl Friston, Morten L. Kringelbach, Gustavo Deco
bioRxiv 2022.01.06.475196; doi: https://doi.org/10.1101/2022.01.06.475196
or here
Deco, G., Cruzat, J., Cabral, J., Tagliazucchi, E., Laufs, H., Logothetis, N. K., & Kringelbach, M. L. (2019). Awakening: Predicting external stimulation to force transitions between different brain states. Proceedings of the National Academy of Sciences, 116(36), 18088-18097.
