4923.sagews

M,Fc,Fn,Vs_day,Vm,Vd,ks,K,Km,Kd,kin,kout,n=var('M Fc Fn  Vs_day Vm Vd ks K Km Kd kin kout n')
# M = function('M',t)
# Fc = function('Fc',t)
# Fn = function('Fn',t)

Vs_day = 1.5
Vs_light = 2.0
Vm = 1.5
Vd = 1.0
ks = 0.5
K = 0.2
Km = 0.15
Kd = 0.15
kin = 0.02
kout = 0.1
n=4

f1 =Vs_day*(K^n/(K^n+Fn^n))-Vm*(M/(Km+M))
show(f1)

$$\renewcommand{\Bold}[1]{\mathbf{#1}}-\frac{1.50000000000000 \, M}{M + 0.150000000000000} + \frac{0.00240000000000000}{\mbox{Fn}^{4} + 0.00160000000000000}$$

f2 =  ks*M - Vd*(Fc/(Kd+Fc))-kin*Fc+kout*Fn
show(f2)

$$\renewcommand{\Bold}[1]{\mathbf{#1}}-0.0200000000000000 \, \mbox{Fc} + 0.100000000000000 \, \mbox{Fn} + 0.500000000000000 \, M - \frac{\mbox{Fc}}{\mbox{Fc} + 0.150000000000000}$$

f3 = kin*Fc - kout*Fn
show(f3)

$$\renewcommand{\Bold}[1]{\mathbf{#1}}0.0200000000000000 \, \mbox{Fc} - 0.100000000000000 \, \mbox{Fn}$$

from sage.calculus.desolvers import desolve_odeint

f = [f1,f2,f3]
ci=[0.3,0.1,0.2]
t=srange(0,100,0.2)
v=[M,Fc,Fn]
sol=desolve_odeint(f,ci,t,v)

p=line(sol)
p.show()

show(f1)

$$\renewcommand{\Bold}[1]{\mathbf{#1}}-\frac{1.50000000000000 \, M\left(t\right)}{M\left(t\right) + 0.150000000000000} + \frac{0.00240000000000000}{{\rm Fn}\left(t\right)^{4} + 0.00160000000000000} - D[0]\left(M\right)\left(t\right) = 0$$

sol=desolve_odeint(f,ci,t,v,rtol=1e-3,atol=1e-4,h0=0.1,hmax=1,hmin=1e-4,mxstep=1000,mxords=17)

$$\renewcommand{\Bold}[1]{\mathbf{#1}}0.0200000000000000 \, {\rm Fc}\left(t\right) - 0.100000000000000 \, {\rm Fn}\left(t\right) - D[0]\left({\rm Fn}\right)\left(t\right) = 0$$