Kuramoto model

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Alon Sela (Author)

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;;;;;;;;;;;;;;;;;;;;;;;;
;;; Setup Procedures ;;;
;;;;;;;;;;;;;;;;;;;;;;;;


turtles-own [
freq1
freq2
]

to setup
  clear-all
  ;set-default-shape turtles "circle"
  ;; make the initial network of two turtles and an edge
  make-node nobody        ;; first node, unattached
  make-node turtle 0      ;; second node, attached to first node
  reset-ticks
end 

;;;;;;;;;;;;;;;;;;;;;;;
;;; Main Procedures ;;;
;;;;;;;;;;;;;;;;;;;;;;;

to go
  ;; new edge is green, old edges are gray
  ask links [ set color gray ]
  make-node find-partner         ;; find partner & use it as attachment
                                 ;; point for new node
  tick
  if layout? [ layout ]
end 

;; used for creating a new node

to make-node [old-node]
  crt 1
  [
    set color red
    set shape "arrow"
    set heading random 360
    set size 3
    set freq1 (random 100) / 10
    if old-node != nobody
      [ create-link-with old-node [ set color green ]
        ;; position the new node near its partner
        move-to old-node
        fd 8
      ]
  ]
end 

;; This code is the heart of the "preferential attachment" mechanism, and acts like
;; a lottery where each node gets a ticket for every connection it already has.
;; While the basic idea is the same as in the Lottery Example (in the Code Examples
;; section of the Models Library), things are made simpler here by the fact that we
;; can just use the links as if they were the "tickets": we first pick a random link,
;; and than we pick one of the two ends of that link.

to-report find-partner
  report [one-of both-ends] of one-of links
end 

;;;;;;;;;;;;;;
;;; Layout ;;;
;;;;;;;;;;;;;;

;; resize-nodes, change back and forth from size based on degree to a size of 1

to resize-nodes
  ifelse all? turtles [size <= 1]
  [
    ;; a node is a circle with diameter determined by
    ;; the SIZE variable; using SQRT makes the circle's
    ;; area proportional to its degree
    ask turtles [ set size sqrt count link-neighbors ]
  ]
  [
    ask turtles [ set size 1 ]
  ]
end 

to layout
  ;; the number 3 here is arbitrary; more repetitions slows down the
  ;; model, but too few gives poor layouts
  repeat 3 [
    ;; the more turtles we have to fit into the same amount of space,
    ;; the smaller the inputs to layout-spring we'll need to use
    let factor sqrt count turtles
    ;; numbers here are arbitrarily chosen for pleasing appearance
    layout-spring turtles links (1 / factor) (7 / factor) (1 / factor)
    display  ;; for smooth animation
  ]
  ;; don't bump the edges of the world
  let x-offset max [xcor] of turtles + min [xcor] of turtles
  let y-offset max [ycor] of turtles + min [ycor] of turtles
  ;; big jumps look funny, so only adjust a little each time
  set x-offset limit-magnitude x-offset 0.1
  set y-offset limit-magnitude y-offset 0.1
  ask turtles [ setxy (xcor - x-offset / 2) (ycor - y-offset / 2) ]
end 

to-report limit-magnitude [number limit]
  if number > limit [ report limit ]
  if number < (- limit) [ report (- limit) ]
  report number
end 

to-report sinheading [heading1 heading2]
     if debug?
        [write "from reporter " print heading1
         write "from reporter "  print heading2
         ]
     let temp1 sin(heading1 - heading2)
     report temp1
end 

to sync
  let k 0.5

  ask turtles [
    if debug? [type "$$$$$$$$$$$$$$$$$$$$$$$$$ : " print who]
    let n 0
    let sin-res 0
    let sigma 0
    let res 0

    fd 0.01
    display
    let my-heading heading
    ;show turtles
    let neig link-neighbors
    ask neig [
      if debug? [
        type "in  neig-loop " ;show who
        write " his heading= " print heading
        write  " my heading = "print my-heading
        ]
      set sin-res sinheading heading my-heading
      ;let sum-heading (sum-heading + sinheading )

      set sigma (sigma + sin-res)
      set n (n + 1)
      if debug? [
        write "sin-res= " print sin-res
        write "sigma = " print sigma
        ]
      ]

     set res (k / n * sigma)
     if debug? [
        type "res= "print res
        ]
     rt res
     display
     fd 1
     bk 1
     ifelse (heading > 0 ) and (heading < 10)
        [set color yellow]
        [set color red]

    ]
  ask turtles [rt 1]
end 



; Copyright 2005 Uri Wilensky.
; See Info tab for full copyright and license.

There is only one version of this model, created over 2 years ago by Alon Sela.

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Kuramoto model.png	preview	Preview for 'Kuramoto model'	over 2 years ago, by Alon Sela	Download

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Kuramoto model

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