title: The Goodwin model revisited: Hopf bifurcation, limit-cycle, and periodic entrainment.
abstract: The three-variable Goodwin oscillator is a minimal model demonstrating the emergence of oscillations in simple biochemical feedback systems. As a prototypical oscillator, this model was extensively studied from a theoretical point of view and applied to various biological systems, including circadian clocks. Here, we reexamine this model, derive analytically the amplitude equation near the Hopf bifurcation and investigate the effect of a periodic modulation of the oscillator. In particular, we compare the entrainment performance when the free oscillator displays either self-sustained or damped oscillations. We discuss the results in the context of circadian oscillators.
authors: Unité Mixte de Recherche 1011, Université Lille 2, INSERM, Institut Pasteur de Lille, Lille, France. Laboratoire de Physique des Lasers, Atomes, Molécules, Unité Mixte de Recherche 8523, Université Lille 1, CNRS, Villeneuve d'Ascq, France.
authors: Aurore
authors: A
authors: Woller
authors: Didier
authors: D
authors: Gonze
authors: Thomas
authors: T
authors: Erneux
mesh_terms: D001669:Biochemical Phenomena; D057906:Circadian Clocks; D002940:Circadian Rhythm; D025461:Feedback, Physiological; D008954:Models, Biological; D049490:Systems Biology