# gberg_auto.ode
# 
init a=0.00118  ap=1.18  k=0  omeg=-0.19,r=.001 
# domain is reasonably small sqrt(1/d) 
par d=0.177  q=0.5, r0=.001  
# the odes...
a'=ap
ap'=a*k*k-ap/r+a/(r*r)-a*(1-a*a)/d
k'=-k/r-2*k*ap/a-(omeg+q*a*a)/d
phi'=k
b phi
# extras to make it autonomous
omeg'=0
r'=1
# the boundary conditions
# at r=0
bndry  a-r*ap
bndry  k
bndry r-r0
# at r=1
bndry  ap'
bndry  k'
# set it up for the user
@ xhi=1.001,dt=.01,total=1.001,ylo=0
@ parmax=1,autoxmax=1,autoxmin=0,autoymax=1,autoymin=0
aux uc=r*cos(phi)
aux vc=r*sin(phi)
done