Light input
This protocol is extracted from research article:
A mathematical model of circadian rhythms and dopamine
Theor Biol Med Model, Feb 17, 2021; DOI: 10.1186/s12976-021-00139-w

The mechanisms of circadian entrainment to light are still not fully understood. Multiple studies have shown that PER expression is induced by light, likely as a result of increased neural activity [3436]. This idea was used in [21] to incorporate light into their detailed model of the main mammalian circadian clock components. We incorporate light input by using a sinusoidal function (t) where ξ=23 with period 24hr to adjust the transcription rate of P1 so that it varies diurnally.

so Eq. 4 is replaced by

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