Solution characteristics plots for the three systems:
x(t)' = µ*x(t) - x(t)^3
x(t)' = µ*x(t) - x(t)^2
x(t)' = µ + x(t)^2
var('m')
f(m)=m*x-x^3
g(m)=m*x-x^2
h(m)=m+x^2
F=[]; G=[]; H=[]
for m in srange(-5,5,0.5):
F+=[plot(f(m),(x,-3,3))+text(str(SR(f))+" with m="+str(m),(1,-1),color="red")]
G+=[plot(g(m),(x,-3,3))+text(str(SR(g))+" with m="+str(m),(1,-1),color="red")]
H+=[plot(h(m),(x,-3,3))+text(str(SR(h))+" with m="+str(m),(1,-1),color="red")]
show(animate(F)); show(animate(G)); show(animate(H))
  
|
|
|