About BF file


How to import a configuration files for BF

During analysis, it is sometimes necessary to reload the results of previous analysis. Currently, when BF is restarted, the information when BF was last terminated is loaded. For example, in the situation

  • First run: calculated a Hopf bifurcation set of equilibrium point A.
  • Second run: calculated a saddle-node bifurcation set of limit cycle.
  • Third run: calculated a saddle-node bifurcation set of equilibrium point B.
  • Fourth run: calculated the Hopf bifurcation set of equilibrium point A again.

At the fourth start of BF, the initial information on equilibrium point B calculated at the third run of BF is loaded. To resume Hopf bifurcation point search of equilibrium point A conducted in the first run, PP must be restarted to obtain information on equilibrium point A, obtain parameters that cause bifurcation in FIX, and pass the information to BF. When BF is terminated, it is possible to save the current status, including the configuration information, into a file to reduce such inconvenience.

The BF settings are saved as an XML formatted file. (See How to save the configured state of BF.) The following is an example of a BF configured file to calculate the Hopf bifurcation set of a equilibrium point observed in the Hodgkin-Huxley equation.

index.php?plugin=attach&refer=aboutBF_file&openfile=dataBF.png

The following steps are used to load the settings files saved for each condition.

  1. Start up BF (Select Program-> BF from menu bar in FIX)

    index.php?plugin=attach&refer=aboutBF_file&openfile=startBF.png

  2. The following shows the state when BF starts up at first time.

    index.php?plugin=attach&refer=aboutBF_file&openfile=startBF2.png

  3. Select File -> Import -> BF save file.

    index.php?plugin=attach&refer=aboutBF_file&openfile=importBF.png

  4. Start up BF save file selection window.

    index.php?plugin=attach&refer=aboutBF_file&openfile=importBF2.png

  5. Select the BF save file.

    index.php?plugin=attach&refer=aboutBF_file&openfile=importBF3.png

  6. When the file have imported, the saved data are reflected to each field.

    index.php?plugin=attach&refer=aboutBF_file&openfile=importBF4.png



How to save the configured state of BF

During analysis, it is sometimes necessary to reload the results of previous analysis. Currently, when BF is restarted, the information when BF was last terminated is loaded.

For example, in the situation

  • First run: Calculated the period-doubling bifurcation set of a fixed point A.
  • Second run: Calculated the Neimark-Sacker bifurcation set of a 3-periodic point B.
  • Third run: Calculated the saddle-node bifurcation set of a fixed point A.
  • Fourth run: Calculated the Neimark-Sacker bifurcation set of the 3-periodic point B again.

At the fourth start of BF, information on the saddle-node bifurcation set of the fixed point A calculated at the third run of BF is loaded. If the information regarding the calculation of the Neimark-Sacker bifurcation set of the 3-periodic point B is saved, it can be reused for recalculation at another time.

Therefore, it is possible to save the current status when terminating BF. To save the configuration information into a file, follow the steps shown below.

  1. Select File -> Export -> BF save file.

    index.php?plugin=attach&refer=aboutBF_file&openfile=exportBF.png

  2. Write the save file name. The default extension is .bfd. It's also able to change the extension.

    index.php?plugin=attach&refer=aboutBF_file&openfile=exportBF2.png

  3. The produced file is an XML formatted file as follows:

    index.php?plugin=attach&refer=aboutBF_file&openfile=exportBF3.png



How to import an initial value files edited as a text file

0 is the input for all Initial state fields and 1 is the input for all Parameters fields (figure below) when starting for the first time. Correct information on the attractor to be analyzed must be given in the Initial state and Parameters fields when searching for bifurcation points. This indicates that information such as the values of the state variables, the parameters, the period of a periodic solution, and the return time of a limit cycle, and the configuration of Poincare section are necessary. Although such information can be manually entered from a GUI panel, the contents of a file can be reflected in the respective fields by making a text file following the rules below and importing the file, at least for values of state variable and parameters.

index.php?plugin=attach&refer=aboutBF_file&openfile=startBF3.png

  1. Prepare a text file describing parameters and state variables in this order.*1.Check the order of the parameters using a web browser.*2 State variables are placed from above in the order x[1], x[2], ・・・, x[n].

    index.php?plugin=attach&refer=aboutBF_file&openfile=importBF5.png

  2. Select File -> Import -> Text data.

    index.php?plugin=attach&refer=aboutBF_file&openfile=importBF6.png

  3. Select the text file from the file selection window, and import the file.

    index.php?plugin=attach&refer=aboutBF_file&openfile=importBF7.png

  4. The state after the import are reflected to the field of the state variables and parameters.

    index.php?plugin=attach&refer=aboutBF_file&openfile=importBF8.png

Actually, knowledge of only state variable and parameter variables does not mean FIX will operate normally. Additional information is necessary, such as the period of a periodic solution or the return time of a limit cycle. Usage of this mode is meaningful only if such necessary additional information is known. If not, this mode should not be used.



How to produce the text file composed of initial values and parameters

This is how to produce a text file composed of a list of state variables and parameters.

  1. Assume that the values in the fields of Initial states and Parameter in the Main panel were the values in the following figure.

    index.php?plugin=attach&refer=aboutBF_file&openfile=exportBF4.png

  2. Select File -> Export -> Text Data.

    index.php?plugin=attach&refer=aboutBF_file&openfile=exportBF5.png

  3. Write the save file name. The default extension is .iv. It's also able to change the extension.

    index.php?plugin=attach&refer=aboutBF_file&openfile=exportBF6.png

  4. After Export, the following text file is produced.

    index.php?plugin=attach&refer=aboutBF_file&openfile=exportBF7.png



How to import initial conditions to run BF

The following figure shows a situation when BF is started right after a Project is generated. Arbitrary values are input in the fields of Initial states and Parameters. BF cannot run from this state, and apropriate initial conditions must be given. FIX is used to find an initial bifurcation point. The following steps are used to load into BF the values of the state variables and the parameters of an initial bifurcation point found using FIX.

  1. Find an initial bifurcation point with a numerical calculation using FIX, and export the condition from FIX. For the steps, see How to pass information of the detected bifurcation point to BF.
  2. Start up BF as FIXProgram -> BF.

    index.php?plugin=attach&refer=aboutBF_file&openfile=startBF.png

  3. The following shows the state when BF starts up at first time.

    index.php?plugin=attach&refer=aboutBF_file&openfile=startBF2.png

  4. Select Tools -> Import initial BF point.

    index.php?plugin=attach&refer=aboutBF_file&openfile=FIXtoBF.png

  5. The attractor information is imported to each fields.

    index.php?plugin=attach&refer=aboutBF_file&openfile=FIXtoBF2.png

Aside from the values of the state variables and parameters, the following necessary information can also be transferred from FIX to BF:

  1. Is the bifurcation the bifurcation of an equilibrium point, or the bifurcation of a limit cycle/periodic solution (periodic point) ?
  2. In case of a limit cycle, where is the Poincare section configured ?
  3. What is the return time of the limit cycle ?
  4. What type of periodic point is this ?
  5. What type of ODE Solver was used ?



How to save various information as data when a bifurcation set is calculated

When a bifurcation set is calculated, it may need to know information later, such as parameters to make a bifurcation diagram, the values of the state variables and the eigenvalues. Various information of the calculations can be saved as data. The following steps show how to to save the various information as data when a bifurcation point is calculated.

  1. Check the checkbox in Output in the BF main panel. In the default settings when first started up BF, the checkbox is checked.

    index.php?plugin=attach&refer=aboutBF_file&openfile=saveDATA.png

  2. Input a File name. In default settings, the data file is saved as bf.out. The file name can be changed into something easier to identify (for example, a name related to the bifurcation set).

    index.php?plugin=attach&refer=aboutBF_file&openfile=saveDATA2.png

    (a) Default settings

    index.php?plugin=attach&refer=aboutBF_file&openfile=saveDATA3.png

    (b) For example, for data on the Hopf bifurcation set of an equilibrium point, change the name to hopf.out .

  3. Start the calculation of the bifurcation set. Click the Start Button. Various information related to the calculation will be displayed in the list box.

    index.php?plugin=attach&refer=aboutBF_file&openfile=saveDATA4.png

  4. Data is saved in the BF_data directory in the Project directory.

    index.php?plugin=attach&refer=aboutBF_file&openfile=saveDATA5.png

  5. The data is a text formatted file as shown below.

    index.php?plugin=attach&refer=aboutBF_file&openfile=saveDATA6.png

The data is described in the following order:

  • The header information starting from # (used in bifurcation plot generation tool BFP)
  • Iterations to convergence in the Newton method, para(X), para(Y), x[1], x[2],・・・,x[n], first eigenvalue (real part) , first eigenvalue (imaginary part), first eigenvalue (absolute value), ・・・, ・・・, n-th eigenvalue (real part), n-th eigenvalue (imaginary part), n-th eigenvalue (absolute value), Jacobian, period.
  • For a bifurcation set in an equilibrium point system, there is no period, and therefore zero is always displayed.
  • For a limit cycle, note that the period is the return time of the limit cycle.
  • For a non-autonomous system, time index.php?plugin=attach&refer=aboutBF_file&openfile=eq_img01.gif (for a index.php?plugin=attach&refer=aboutBF_file&openfile=eq_img02.gif-periodic solution) is displayed
  • For a discrete system, the period is not displayed.




*1 This file is also text files produced by using non-BunKi program (However, to run FIX, it is not enough to prepare the set of the values of parametes and state variables. The additonal information such as the configuration of the Poincare section, the period of a limit cycle, a periodic solution or a periodic point must be set.). The text file can be also produced from PP using a method How to produce a text file composed of initial values and parameters.
*2 See also How to check the generated system.

Attach file: fileeq_img02.gif 195 download [Information] fileeq_img01.gif 193 download [Information]

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Last-modified: 2009-07-23 (Thu) 20:13:30 (3310d)