Download presentation

Presentation is loading. Please wait.

Published byAbel Ferrington Modified over 2 years ago

1
**Introduction to AUTO 20001 AUTO 2000 ~ numerical bifurcation software**

Presented by Patrick Longhini E.J. Doedel, R.C. Paffenroth, A.R. Champneys, T.F. Farirgrieve, Yu. A Kuznetsov, B. Sandstede & X.Wang (2001) “AUTO 2000: Continuation and bifurcation software for ODEs (with HomCont)” Technical Report, Caltech, Feb. 2001

2
**Getting Started Download**

The AUTO manual gives details on how to install the program on your Linux/UNIX based machine. AUTO can do bifurcation analysis on a system of ordinary differential equations (ODEs) of the form

3
**Main AUTO files The equation-file xxx.c The constants-file c.xxx**

Contains the C subroutines func, stpnt, bcnd, icnd, … func: defines the function f(u,p) stpnt: defines the starting solution (u,p) The constants-file c.xxx Controls the dynamics of AUTO

4
Example 1: abc reaction This demo illustrates the computation of stationary solutions, Hopf bifurcations and periodic solutions in the A B C reaction (Doedel & Heinemann (1983)).

5
**Solution of Example abc**

6
**Basic Steps: Step 1: step up abc.c and c.abc**

Step 2: first run -- stationary solutions Step 3: restart at hopf and compute periodic solutions

7
**Define system: abc.c Required Subroutines Parameters**

Initial Conditions

8
**Define constants: c.abc**

Run 1: save as c.abc.1 Constants briefly described in: auto2000_quick_ref.pdf

9
MOST USED CONSTANTS

10
Command Line To begin type auto 3 80

12
**save(‘abc’) Using save(‘abc’) you get 3 output files**

b.abc bifurcation branches s.abc solution d.abc dynamics (stability) Relating labels to output file.

13
b.abc

14
d.abc

15
Using the comand: plot(‘abc’)

16
**Looking at the solution for label 7**

17
**Example 2: lor.c Starting an orbit from numerical data**

with p1 = 280, p2 = 8/3 and p3 = 10. Numerical data must have one complete periodic oscillation which is contained in lor.dat us(‘lor’) creates AUTO output file s.dat

18
Creating file: xxx.dat Use fprintf to print the data to a file. Make sure that you only have one period.

19
time u u u3 lor.dat

20
Command line steps: Show how to write a Makefile to run command line steps. This is better because you can running all the steps with one command and keep track of your work.

21
Makefile

23
**Plotting using Plaut @p lor**

Type: Commands d3 (show stability) then BD0 (default settings) Appendix B of manual contains all commands

24
**Useful commands: (using command mode)**

@fl lor – list Floquet multipliers in d.lor @ev abc – list eigenvalues of the Jacobian d.abc @lp xxx, lists limit points, branch points and hopf bifurcations, respectively.

25
lor

26
**Graphical User Interface.**

Type @auto or its Appendix C of manual contains help for GUI

27
**Other useful tools xppaut www.math.pitt.edu/~bard/xpp/xpp.html**

Solves ODEs,DDEs,also AUTO built in winpp Windows version of xppaut but used LOCBIF instead of AUTO matcont allserv.rug.acbe/~ajdhooge/research.html Continuation software in Matlab July 9th 2004 (lastest version) DDE-BIFTOOL Matlab package for numerical bifurcation analysis of delay equations

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google