TITLE Poincare Oscillator
:  National Biomedical Simulation Resource, 8-4-89
:  Reference - Glass and Mackey, From Clocks to Chaos, Princeton
:    University Press, 1988, Chapter 2
:  Default output - Spiral (phase plot) starting near the origin
:    ending with a stable radius of 1.  Note that the small value
:    of delta_t was chosen to make the model run slowly.  This
:    value can be increased to increase the speed on slower machines.
PARAMETER
{
  r0 = .1
  a  =  2
  delta_t = .001
}
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' = a * r * (1 - r)
  theta' = 6.2832
}
BREAKPOINT
{
  SOLVE eqns METHOD heun
  x = r * cos(theta)
  y = r * sin(theta)
}