FIX (Fixed Point Tracker)

What's this ?

This tool is used to check the stability of an equilibrium point or a limit cycle in a set of ordinary differential equations in an autonomous system, or the stability of periodic solutions in a set of ordinary differential equations or the stability of a set of fixed (or periodic) points in a set of difference equations. Based on the approximate values of equilibrium points or fixed points obtained by PP, the precise position is calculated using the Newton method. By evaluating the eigenvalues of the variational equations with respect to the attractor, this tool can detect bifurcation points when the system parameters change.

Main Panel

• Mode(only for the autonomous system)
• Selects equilibrium points or a limit cycle as an operation of FIX tool.

• Initial states
• Configuration of State variables and the other parameters
• x[1], x[2], ... , x[n] : Each value of the state variables
• Section: State variables set as the Poincare section (Only for the limit cycle observed in the autonomous system)
• Period : Period of a periodic point in Poincare map (non-autonomous system, discrete system)
• Return time : Return time of a limit cycle (Only for the limit cycle of an autonomous system)

(a) In case of the limit cycle observed in an autonomous system.

(b) In case of a non-autonomous system.

(c) In case of a discrete system.
• Parameters
• Configuration of System Parameters and the other parameters
• X : Parameter for a change in the x-axis direction
• Y : Parameter for a change in the y-axis direction
• start : The values of system parameters when FIX starts. If initial values are imported from PP, these values are applied to each field.
• step size : Step sizes of changing parameters. Displayed when X or Y is selected.
• stop : Stop values of the changing parameter. When system parameters become this value, the calculation stops.

• Output file
• File name : Output an information (e.g., the value of system parameters, state variables, eigenvalues, and so on) displayed in the list box to a file (Default configuration is OFF)

• Start, Stop
• Controls when to start/stop calculations.

• ODE Solver(Limited to the autonomous and the non-autonomous systems)
• Displays the name of the Solver used to conduct numerical integration. For details refer to Setting.

• List Box
• Displays the calculation results. The numbers displayed correspond to the following respectively:
```Number of iterations para(X) para(Y) x[1], x[2], ・・・, x[n] |
Eigenvalue(real part), Eigenvalue(imaginary part), absolute value |
・・・ |・・・ |（Jacobian)```

• It is possible to reflect the current condition in the respective item fields by right-clicking in this list box*1.

• File
• clear : If selected, clears to the configuration when FIX was started up.~

• Import : Imports previously saved FIX settings and initial condition files*2.
• FIX save file : Imports previously saved FIX configurations (XML file)
• Text data : Imports contents of a text file into Initial states and Parameters fields (text file)

• Export : Exports all current FIX settings or exports initial values and parameters into a text file*3.
• FIX save file : Exports current FIX settings (XML file)
• Text data : Exports data in Initial states and Parameters fields as text data (text file)

• Close : Quit FIX

• Program
• SE : Starts the SE panel for the current Project.
• PP : Starts the PP tool for the current Project.
• FIX : Starts the FIX tool for the current Project.
• BF : Starts the BF tool for the current Project.
• BFP : Starts the tool for making a bifurcation diagram.

• Project
• Change Project: This is used to generate a project other than the current generated project, or to load already existing projects.

• Tools
• Import initial point : Used to retrieve information on equilibrium points or fixed points obtained by PP to each field*4.
• Export BF point : Used to export values consisting of state variables and parameters when bifurcation points are detected to BF*5.

• Setting
• Used to set operation details of Fixed point tracker tool(FIX). The items that can be set depend on the system. Refer to the following for details:
• Help
• Manual : Startup the manual of FIX.
• Select Japanese or English

(a) Selection of the Manual

(b) Start up the FIX manual

• about BunKi：A brief introduction of BunKi.
• Version information, contact lists to developer team, credit, etc．

(b) Display the credit for BunKi

*1 For details, refer to How to restart FIX when the stop button is pressed
*2 For details, refer to How to import an initial setting for FIX and How to import an initial value from a text file.
*3
*4 For details, refer to How to import an initial value to start FIX.
*5 For details, refer to How to import an initail value to start BF.

Last-modified: 2009-07-23 (Thu) 20:13:30 (3623d)