Bifurcation diagram for the logistic map
Model was written in NetLogo 6.0.1
•
Viewed 883 times
•
Downloaded 38 times
•
Run 0 times
Do you have questions or comments about this model? Ask them here! (You'll first need to log in.)
Info tab cannot be displayed because of an encoding error
Comments and Questions
Please start the discussion about this model!
(You'll first need to log in.)
Click to Run Model
globals [ ;; setting the globals for the model functioning mylist-x mylist-r num-iterations axis F-const? ] breed [ m-turtles m-turtle ] ;; these are turtles to be ploted on ;; on bifurcation diagram patches-own [ ;; properties of the patches used alpha ;; to set up X and Y axes omega ] to setup ;; general setup procedure ca set mylist-x list (0) (0.5) ;; setting the list for turtles x-coordinates set mylist-r list (0) (0.95) ;; setting the list for turtles y-coordinates create-axis ;; creating coordinates axes setup-alpha ;; and their components setup-beta-omega set num-iterations 20325 ;; this is the max number of iterates which ;; "keeps" the results of iterations in the ;; limits of the model world reset-ticks end to create-axis ask patches with [ pxcor = 0 ] [ set pcolor white ] ask patches with [ pycor = 0 ] [ set pcolor white ] end to setup-alpha ask patch -4 -4 [ set plabel "0" set plabel-color white ] ask patch -4 190 [ set plabel "f (x)" set plabel-color white ] ask patch 390 -7 [ set plabel "r-parameter" set plabel-color white ] end to setup-beta-omega ask patch 105 5 [ set plabel "1.0" set plabel-color white ] ask patch 205 5 [ set plabel "2.0" set plabel-color white ] ask patch 255 5 [ set plabel "2.5" set plabel-color white ] ask patch 305 5 [ set plabel "3.0" set plabel-color white ] ask patch 355 5 [ set plabel "3.5" set plabel-color white ] ask patch 395 5 [ set plabel "4.0" set plabel-color white ] ask patch 10 100 [ set plabel "0.5" set plabel-color white ] ask patch 10 195 [ set plabel "1.0" set plabel-color white ] end to go ;; procedure of iteration set mylist-x lput result mylist-x ;; generation of the list with repeat 50 [set mylist-x lput result mylist-x] ;; x-coordinates of turtles set mylist-r lput result-r mylist-r ;; generation of the list with ;; x-coordinates of turtles if ticks >= Num-iterations [ stop ] ;; condition for stopping the model once ;; the preset number of iterations is reached create-m-turtles 1 [ ;; creating a turtle every iteration/tick set color green ;; and ploting it according to the coordinates set shape "circle" ;; as values in the respective lists set size 0.5 set xcor (last mylist-r) * 100 set ycor (last mylist-x) * 200 ] tick end to-report result ;; reports the result of iterations report last mylist-r * last mylist-x * (1 - last mylist-x) end to-report result-r ;; reports the result of r-increments with every iteration/tick report last mylist-r + 0.00015 end to mark ;; marking the bifurcations by creating red color turtles ;; in respective zones if ticks >= 20320 [ ;; condition that makes respective button active only after ;; iterations are completed crt 1 [ set color red set shape "circle" set size 2 set xcor 300 set ycor 133 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 354 set ycor 164 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 345 set ycor 170 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 354 set ycor 177 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 345 set ycor 88 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 354 set ycor 105 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 354 set ycor 73 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 356.37 set ycor 69.43 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 356.41 set ycor 74.92 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 356.43 set ycor 98.16 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 356.47 set ycor 110.93 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 356.42 set ycor 161.49 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 356.46 set ycor 167.02 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 356.44 set ycor 176.12 ] crt 1 [ set color red set shape "circle" set size 2 set xcor 356.48 set ycor 178.16 ] ] end to mark-pw ;; marking a periodic window if ticks >= 20320 [ ask patches with [ pxcor = 380 ] [set pcolor red] ask patches with [ pxcor = 390 ] [set pcolor red] ] end to calculate-feigenbaum-constant ;; procedure ref. to Feigenbaum's constant: ploting ;; vertical lines aligned to bifurcations and marking ;; the distance between consecutive period-doublings with "L" if ticks >= 20320 [ ;; condition that makes the procedure valid after the set F-const? true ;; preset number of iterations ask patches with [ pxcor = 300 ] [set pcolor white] ask patches with [ pxcor = 345 ] [set pcolor white] ask patches with [ pxcor = 354 ] [set pcolor white] ask patches with [ pxcor = 356 ] [set pcolor white] ask patch 198 -7 [ set plabel "L0" set plabel-color yellow ] ask patch 330 -7 [ set plabel "L1" set plabel-color yellow ] ask patch 355 -7 [ set plabel "L2/L3" set plabel-color yellow ] ask patch 100 155 [ set plabel "Feigenbaum's constant = Li / Li+1" set plabel-color yellow ] ] end to-report F-constant-1 ;; procedure for calculation of the 1st Feigenbaum's constant if F-const? = true ;; based on x-coordinates of the turtles located in the bifurcations zones [ ;; 'bifurcations zones' report (([xcor] of turtle 17294) - ([xcor] of turtle 16688)) / (([xcor] of turtle 17422) - ([xcor] of turtle 17292)) ] end
There is only one version of this model, created about 7 years ago by Victor Iapascurta.
Attached files
File | Type | Description | Last updated | |
---|---|---|---|---|
Bifurcation diagram for the logistic map.png | preview | Preview for 'Bifurcation diagram for the logistic map' | about 7 years ago, by Victor Iapascurta | Download |
This model does not have any ancestors.
This model does not have any descendants.