Lotka-Volterra Equation: Phase Plane

globals [
mylist-x
mylist-y
  sheep-birth-rate
  predation-rate
  predator-efficiency
  wolf-death-rate
  sheep
  wolves
  dt
]

to setup
  ;clear-all
  clear-globals
  clear-ticks
  clear-patches
  clear-all-plots
  ask patches with [ pxcor = 0 ] [  set pcolor white ]
  ask patches with [ pycor = 0 ] [  set pcolor white ]
  setup-coordinates
  set mylist-x list 0 (sheep)
  set mylist-y list 0 (wolves)
  system-dynamics-setup
  system-dynamics-do-plot
end 

to system-dynamics-setup
  reset-ticks
  set dt 0.009
  set sheep-birth-rate sheep-birth-rate-slider
  set predation-rate predation-rate-slider
  set predator-efficiency .8
  set wolf-death-rate 0.15
  set sheep sheep-num
  set wolves wolves-num
end 

to clear-picture
  ca
end 

to go
  system-dynamics-go
  system-dynamics-do-plot
  set mylist-x lput result-x mylist-x
  set mylist-y lput result-y mylist-y
  crt 1 [
    set color select-phase-plot-color
    set xcor (last mylist-x * 0.15)
    set ycor (last mylist-y * 0.15)
    set size 0.5
    set shape "circle"
  ]

  if ticks >= 300 [ stop ]
end 

to system-dynamics-go

  let local-sheep-births sheep-births
  let local-sheep-deaths sheep-deaths
  let local-wolf-births wolf-births
  let local-wolf-deaths wolf-deaths

  let new-sheep max( list 0 ( sheep + local-sheep-births - local-sheep-deaths ) )
  let new-wolves max( list 0 ( wolves + local-wolf-births - local-wolf-deaths ) )
  set sheep new-sheep
  set wolves new-wolves

  tick-advance dt
end 

to-report sheep-births
  report ( sheep-birth-rate * sheep
  ) * dt
end 

to-report sheep-deaths
  report ( sheep * predation-rate * wolves
  ) * dt
end 

to-report wolf-births
  report ( wolves * predator-efficiency * predation-rate * sheep
  ) * dt
end 

to-report wolf-deaths
  report ( wolves * wolf-death-rate
  ) * dt
end 

to-report result-x
  report sheep
end 

to-report result-y
    report  wolves
end 

to setup-coordinates
  ask patch -5 5
  [ set plabel "0"
    set plabel-color white ]

  ask patch -7 160
  [ set plabel "1000"
    set plabel-color white ]

  ask patch -7 80
  [ set plabel "500"
    set plabel-color white ]

  ask patch 160 -5
  [ set plabel "1000"
    set plabel-color white ]

  ask patch 320 -5
  [ set plabel "2000"
    set plabel-color white ]

  ask patch -5 -48
  [ set plabel "-50"
    set plabel-color white ]

  ask patch -40 -5
  [ set plabel "-50"
    set plabel-color white ]

  ask patch -10 193
  [ set plabel "Wolves"
    set plabel-color blue ]

  ask patch 380 -10
  [ set plabel "Sheep"
    set plabel-color red ]
end 

to system-dynamics-do-plot
  if plot-pen-exists? "sheep" [
    set-current-plot-pen "sheep"
    plotxy ticks sheep
  ]
  if plot-pen-exists? "wolves" [
    set-current-plot-pen "wolves"
    plotxy ticks wolves
  ]
end