import matplotlib.pyplot as plt

import numpy as np

from scipy.integrate import odeint

def pend $,$ beta, alpha$)$:

$x,Y,Z=y$

$n=1000$

$K=0\mathrm{.}5$ #change $K$ value and see what happens

hill$\_$theta $=\frac{x^{****}n}{(K^{****}n)+(x^{****}n)}$

hill$\_$omega $=\frac{K^{****}n}{(K^{****}n)+(Y^{****}n)}$

dydt $=[$beta$-$alphahill$\_$theta$-$alphahill$\_$thetaZ$]$

return dydt

beta $=1\mathrm{.}0,$ #production rate

alpha $=1\mathrm{.}0,$ #removal parameter

y $=[0,0,0],$ #initial conditions

$t=np.$ linspace $(0,10,51)$ #time

sol $=$ odeint $($pend$,$ yo$,$ t$,$ args$=($beta$,$ alpha$)$