Child of Urban (System Dynamics)

;; System dynamics model globals
globals [
  ;; stock values
  y1
  y2
  y3
  ;; size of each step, see SYSTEM-DYNAMICS-GO
  dt
  ;; Additional global variable
  sigma
  r
  b
]

;; Initializes the system dynamics model.
;; Call this in your model's SETUP procedure.

to system-dynamics-setup
  reset-ticks
  set dt 0.001
  ;; initialize stock values
  set y1 random-float 0.0
  set y2 random-float 1.0
  set y3 random-float 0.0
  ;; initialize sigma
  set sigma 10.0
  ;; initialize r
  set r 28.0
  ;; initialize b
  set b 2.6667
end 

;; Step through the system dynamics model by performing next iteration of Euler's method.
;; Call this in your model's GO procedure.

to system-dynamics-go

  ;; compute variable and flow values once per step
  let local-y1' y1'
  let local-y2' y2'
  let local-y3' y3'

  ;; update stock values
  ;; use temporary variables so order of computation doesn't affect result.
  let new-y1 ( y1 + local-y1' )
  let new-y2 ( y2 + local-y2' )
  let new-y3 ( y3 + local-y3' )
  set y1 new-y1
  set y2 new-y2
  set y3 new-y3

  tick-advance dt
end 

;; Report value of flow

to-report y1'
  report ( sigma * (y2 - y1)
  ) * dt
end 

;; Report value of flow

to-report y2'
  report ( y1 * (r - y3) - y2
  ) * dt
end 

;; Report value of flow

to-report y3'
  report ( y1 * y2 - b * y3
  ) * dt
end 

;; Plot the current state of the system dynamics model's stocks
;; Call this procedure in your plot's update commands.

to system-dynamics-do-plot
  if plot-pen-exists? "y1" [
    set-current-plot-pen "y1"
    plotxy ticks y1
  ]
  if plot-pen-exists? "y2" [
    set-current-plot-pen "y2"
    plotxy ticks y2
  ]
  if plot-pen-exists? "y3" [
    set-current-plot-pen "y3"
    plotxy ticks y3
  ]
end