Talk:Goodwin model (biology)

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The original Goodwin model is an odd one. It only has two variables so it's not a classical feedback oscillator that requires three. In addition, as the Wikipedia article suggests, there are no stable limit cycles, meaning that changes to the initial conditions will change the amplitude of the oscillation (this doesn't happen in a feedback amplifier). The oscillator acts more like a harmonic oscillator and in fact, the eigenvalues at the unstable focus are pure imaginary which is consistent with this idea. Rhodydog (talk) 20:16, 8 June 2022 (UTC)[reply]

Actually Goodwin originally described a three variable model in his 1963 book (freely available as doi:10.5962/bhl.title.6268). However in the derivation of the equations he eliminated the variable M (metabolite) with the quasi-steady state approoximation, leaving the model only with X (mRNA) and Y (protein). Later on, he added M again in order to get rid of the marginal stability of the 2-variable. I will add some text later on as this page is in need of a lot of care. Gepasi (talk) 01:45, 24 April 2023 (UTC)[reply]

Good to know. The page definitely needs some attention. Rhodydog (talk) 23:16, 25 April 2023 (UTC)[reply]