###########################################################
#
#  Chemical Oscillator Model for concentrations u and v
#
#  physical parameters a,b > 0 
#
#
#  For b=0.5, a Hopf bifurcation occurs at a=0.1823. 
#  For a < 0.1823, TrDF >0 and the sole equilibria is
#  unstable. Stable periodic orbits emerge and surround
#  the unstable periodic orbit  - making it a
#  supercritical Hopf bifurcation.
#
#  For the AUTO calculations generating the bifurcation
#  diagram in a (with b fixed at 0.5) use a range of
#  0 < a < 0.5 with 0 < u < 5. This gives a reasonably 
#  scaled diagram.
#
#  equilibria   (U,V) = (a+b,b/(a+b)^2)
#
#
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#
#       parameter values defining model
#
p a=0.5,b=0.5
#
#       function definitions
#
f1(u,v)=a-u+u^2*v
f2(u,v)=b-u^2*v
#
#      differential equations
#
u'=f1(u,v)
v'=f2(u,v)
#
#      initial conditions (optional)
#
u(0)=1
v(0)=1
#
#
# Numerical and graphical parameters go here:
#
#
@ total=100,xlo=0,xhi=40,ylo=0,yhi=4,dt=0.01,maxstor=20000
#
d