about BFP

How to draw Bifurcation diagrams from data

In the case that the calculation of the bifurcation have finished by using BF, the user has to display the result as a bifurcation diagram. Data are include values of system parameters, state variables, eigenvalues, etc. Actually, when drawing a 2-parameter bifurcation diagram, the user has to make a data set consisting of bifurcation parameter values and display them by using a plotting software. BFP is a tool that displays 2-parameter bifurcation diagrams from calculated data. The calculated data are saved to the BF_data directory in the Project directory.


  1. Select Program -> BFP from the menu of BF tool(or other tools), and then start up BFP.


  2. Select File -> Add Files or click the + buttonĄ„ Start up the Select Files to Open window.



  3. Select data to draw the 2-parameter bifurcation. In the selection of multiple data sets, click Shift + files or Ctrl + files.


  4. Click Plot button, and then display the bifurcation diagram.



How to display kinds of bifurcation set

When the user draws a bifurcation diagram, it is possible to display symbols with each curve to explicit the kinds of bifurcations. The correspondence between the symbols and bifurcations is as follows:

List of the symbols
Saddle-node bifurcation of an equilibrium pointeSN
Hopf bifurcation of an equilibrium pointH
Pitch-fork bifurcation of an equilibrium pointePf
Saddle-node bifurcation of a fixed pointSN
Period-doubling bifurcation of a fixed pointPD
Neimark-Sacker bifurcation of a fixed pointNS
Pitch-fork bifurcation of a fixed pointPf

  1. Select Setting -> Preferences.


  2. Start up Preferences window


  3. Check the box of Set Type Name to Bifurcation Curve.


  4. Added symbols to each bifurcation curve.


How to exchange the parameter drawing as X-axis for that of Y-axis

It is possible to switch the X-axis and Y-axis parameters when the user draws a two-parameter bifurcation diagram. The method is as follows:

  1. Select Setting -> Preferences.


  2. Start up Preferences window.


  3. Check the box of Exchange the parameter of X-axis for that of Y-axis.


  4. Before and after the exchange, the parameters of x-axis and of y-axis are exchanged.


    (a) Before the axes exchange


    (b) After the axes exchange

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Last-modified: 2009-07-23 (Thu) 20:13:30 (3767d)