; this script solves numerically prob. 7.1.9
; from Strogatz "Nonlinear Sys. and Chaos"

	i   = dcomplex(0.0, 1.0d0)
	one = dcomplex(1.0d0, 0d0)
	time = 500.d0 & dt = 0.004d0
	N = 1L*time/dt
	pic = complexarr(N+1L) 
	dt05 = 0.5d0*dt
;-----changes in the inteval [0,1]
 for is = 5,100,5 do begin
	s = is*0.01d0
	pic = 0*pic ; zero the storage 
	r = one		; initial position 

  for k = 0L, N-1L do begin			; 2nd order integrator	
	r0 = r
	rdot0 = i*(1-r)-s*r/abs(r)      ; first r.h.s. evaluation
	r = r + rdot0*dt				; predictor step
	rdot1 = i*(1-r)-s*r/abs(r)      ; 2nd r.h.s. evaluation
	r = r0 + (rdot0+rdot1)*dt05		; corrector step w/averaged r.h.s.
	pic(k) = r 						; store trajectory
  endfor
 
;----plot trajectory
 if(is EQ 5)then plot,real_part(pic(0:N-1)),imaginary(pic(0:N-1)),charsize=2 $
		,psym=3,yrange=[0.,0.7],xrange=[0.,1.1],xtitle='X',ytitle='Y'
 oplot,real_part(pic(0:N-1)),imaginary(pic(0:N-1)),color=444,psym=4,symsize=0.1
 endfor
end