Strong feedback limit of the Goodwin circadian oscillator

The three-variable Goodwin model constitutes a prototypical oscillator based on a negative feedback loop. It was used as a minimal model for circadian oscillations. Other core models for circadian clocks are variants of the Goodwin model. The Goodwin oscillator also appears in many studies of coupled oscillator networks because of its relative simplicity compared to other biophysical models involving a large number of variables and parameters. Because the synchronization properties of Goodwin oscillators still remain difficult to explore mathematically, further simplifications of the Goodwin model have been sought. In this paper, we investigate the strong negative feedback limit of Goodwin equations by using asymptotic techniques. We find that Goodwin oscillations approach a sequence of decaying exponentials that can be described in terms of a single-variable leaky integrated-and-fire model. DOI: 10.1103/PhysRevE.87.032722