goodwin

diffeqzoo.ivps.goodwin(*, initial_values=(0.0, 0.0), time_span=(0.0, 25.0), r=10, a1=1.0, a2=3.0, alpha=0.5, k=(1.0,))

Construct the Goodwin Oscillator dynamics.

Describes a mechanism for periodic protein expression described by Goodwin (1965). The first dimension describes the mRNA concentration, the last dimension the protein inhibiting mRNA production, and the remaining dimensions correspond to intermediate protein species. r > 8 leads to oscillatory behavior. It is a n-dimensional ODE initial value problem. The length of the k needs to be len(initial_values)-1.

Common problem for parameter inference, where the posterior has a multimodal distribution.

BibTex for Goodwin (1965)

@article{goodwin1965oscillatory,
    title = {Oscillatory behavior in enzymatic control processes},
    journal = {Advances in Enzyme Regulation},
    volume = {3},
    pages = {425-437},
    year = {1965},
    author = {Brian C. Goodwin},
}