TITLE Oscillator with Hopf Bifurcation
:  National Biomedical Simulation Resource, 8/4/89
:  Reference - Glass and Mackey, From Clocks to Chaos, Princeton
:  University press, Chapter 2.
:  Default output - Three curves starting near radius = 0.5: the first
:    spirals in toward the origin, the second is stable as a circle, the
:    third spirals outward toward a radius of approximately 1.5.  Note
:    that the small delta_t is chosen to make the computation slow for
:    visibility of the curves.  delta_t can be increased on machines where
:    the calculation is too slow.

PARAMETER

{
  r0 = .541196  : Unstable limit = sqr(1 - sqr(1 + c)) for -1 < c < 0
                : Stable limit = sqr(1 + sqr(1 + c)) for c > -1
                : Stable limit = 0 for c < 0
  delta_t = .001
}

STEPPED
{
  c = -.6, -.5, -.4
}

INDEPENDENT
{
  t FROM 0 TO 5 WITH 200
}

PLOT y VS x

ASSIGNED
{
  x FROM -3 TO 3
  y FROM -2.5 TO 2.5
}

STATE
{
  r FROM 0 TO 3
  theta
}

DERIVATIVE eqns
{
  r' = r * (c + 2 * r * r - r * r * r * r)
  theta' = 6.2832
}

BREAKPOINT

{
  SOLVE eqns METHOD heun
  x = r * cos(theta)
  y = r * sin(theta)
}