The Goodwin model is a mathematical model of genetic regulation proposed in 1963 by the British theoretical biologist Brian C. GoodwinGoodwin, B. Oscillatory behavior in enzymatic control processes. Advances in Enzyme Regulation, 3, 1965, pages 425–428. . It describes how a simple negative feedback loop between a gene, its messenger RNA, the corresponding protein and a metabolite can generate sustained oscillations in concentration. It has been used to describe circadian rhythms or enzymatic regulation (such as lactose in bacteria).
Although the original two-variable Goodwin model can sustain oscillations, it possesses no limit cycle: the system is conservative, so its closed orbits form a continuous family and the amplitude of the oscillation depends on the initial conditions rather than converging to a single attracting cycle. In this respect the Goodwin model resembles the Lotka–Volterra equations. Limit cycles do arise in extended formulations of the modelM. Mincheva., M.R. Roussel., Turing-Hopf instability in biochemical reaction networks arising from pairs of subnetworks, Mathematical Biosciences, 240 (2012), 1-11T. Saithong, K. Painter, A. Millar, The contributions of interlocking loops and extensive nonlinearity to the properties of the circadian clocks models, PLOS One 5 (2010) e13867. .
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