Kuramoto model

1 collaborator

Alon Sela (Author)

WHAT IS IT?

The following models shows the Kuramoto model, first proposed by Yoshiki Kuramoto. It is a mathematical model used to describe synchronization of a network of coupled oscillators.

HOW TO USE IT

Press Setup, then Go, the Redo once, untill a network of arrows is presented. when the arrows are in an up direction, they flash. At the initial state, each arrow is in a random direction.

Press Go-Sync, and observe how the networs starts syncronizing. It might take a short while.

THINGS TO NOTICE

The networks seems to spread information as if is was a neural net, but no information is passing, just phase syncronizations.

THINGS TO TRY

Inspect the model at different speed. See how local sync transform to global sync.

EXTENDING THE MODEL

Add different networks. Add a mean vector for the entire network. How is the "leading" oscilator chosen?

NETWORK CONCEPTS

NETLOGO FEATURES

RELATED MODELS

See also Network Example, in the Code Examples section.

CREDITS AND REFERENCES

This model is based on: Kuramoto model

HOW TO CITE

as you want....

Please site the Kuramoto model itself
The adaptation of the kuramoto model in this graphical context from an existing preferential attachment modl was made by Alon Sela, Tel Aviv University.

Comments and Questions

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Click to Run Model

;;;;;;;;;;;;;;;;;;;;;;;;
;;; 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 almost 4 years ago by Alon Sela.

Attached files

File	Type	Description	Last updated
Kuramoto model.png	preview	Preview for 'Kuramoto model'	almost 4 years ago, by Alon Sela	Download

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