# voorbeeld cursus glycolyse
from sage.calculus.desolvers import desolve_odeint
x,y,t=var('x,y,t')
a=0.1
b=0.6
f=[-x+a*y+x^2*y,b-a*x-x^2*y]
p1=plot_vector_field(f,(x,0,2.5),(y,0,2.7))
sol=desolve_odeint(f,[1,2],srange(0,50,0.1),[x,y])
p2=line(zip(sol[:,0],sol[:,1]),color='blue')
sol=desolve_odeint(f,[1.5,2],srange(0,50,0.1),[x,y])
p3=line(zip(sol[:,0],sol[:,1]),color='magenta')
sol=desolve_odeint(f,[1.2,1],srange(0,50,0.1),[x,y])
p4=line(zip(sol[:,0],sol[:,1]),color='red')
p=p1+p4
p.save('limitcycle.eps')
show(p)
