#
#   A system with a subcritical Hopf bifurcation
#   at parameter value a = 0. Use the following 
#   ranges for the diagram:
#
#         -0.05 < a < 0.05        -1 < u < 2
#
#   For a range of a < 0 unstable periodic orbits
#   surround stable equilibria - making it a subcritical
#   Hopf bifurcation.
#
###########################################################
#
#       parameter values defining model
#
p a=0.05,b=1
#
#       function definitions
#
f1(u,v)=a*u+v+u*v+b*u*v^2
f2(u,v)=-u+a*v-u^2+v^2
#
#      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=-2,xhi=4,ylo=-2,yhi=4,dt=0.01,maxstor=20000
#
d