CircadianRhythm

Systems · Continuous · Chem bio systems

Dimension: 5

Equations

\[ \begin{aligned} \dot{y_{0}} &= \frac{2.5 Ki^{n} \left(vmax - vmin\right) \left(vmin + 0.5 \cos{\left(y_{4} \right)} + 0.5\right)}{Ki^{n} + y_{3}^{n}} - \frac{vm y_{0}}{km + y_{0}} \\ \dot{y_{1}} &= - k y_{1} - k_{1} y_{1} + k_{2} y_{3} + ks y_{0} \\ \dot{y_{2}} &= k y_{1} - \frac{vd y_{2}}{kd + y_{2}} \\ \dot{y_{3}} &= k_{1} y_{1} - k_{2} y_{3} - \frac{vdn y_{3}}{kdn + y_{3}} \\ \dot{y_{4}} &= \frac{\pi}{12} \end{aligned} \]

Parameters

parameter	default
Ki	1
k	0.5
k1	0.3
k2	0.15
kd	1.4
kdn	0.4
km	0.4
ks	1
n	4
vd	6
vdn	1.5
vm	0.7
vmax	4.7
vmin	1.0
vs	6

Usage

import tsdynamics as ts

sys = ts.CircadianRhythm()
traj = sys.integrate(final_time=100.0, dt=0.01)

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