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 point eSN Hopf bifurcation of an equilibrium point H Pitch-fork bifurcation of an equilibrium point ePf Saddle-node bifurcation of a fixed point SN Period-doubling bifurcation of a fixed point PD Neimark-Sacker bifurcation of a fixed point NS Pitch-fork bifurcation of a fixed point Pf

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

Last-modified: 2009-07-23 (Thu) 20:13:30 (3650d)