Goodwin model (biology)

In biology, the Goodwin model describes negative feedback oscillators in cellular systems,^[1] for example, circadian rhythms or enzymatic regulation (such as lactose in bacteria). The Goodwin model, though, shows no stable limit cycles.

limit cycles can exist, see references.^[2]^[3] But not in the original Goodwin model which only has two variables.

References

^ Goodwin, B. Oscillatory behavior in enzymatic control processes. Advances in Enzyme Regulation, 3, 1965, pages 425–428. doi:10.1016/0065-2571(65)90067-1
^ M. Mincheva., M.R. Roussel., Turing-Hopf instability in biochemical reaction networks arising from pairs of subnetworks, Mathematical Biosciences, 240 (2012), 1-11
^ T. 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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[1] Goodwin, B. Oscillatory behavior in enzymatic control processes. Advances in Enzyme Regulation, 3, 1965, pages 425–428. doi:10.1016/0065-2571(65)90067-1

[2] M. Mincheva., M.R. Roussel., Turing-Hopf instability in biochemical reaction networks arising from pairs of subnetworks, Mathematical Biosciences, 240 (2012), 1-11

[3] T. 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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