Download presentation

Published byAbel Ferrington Modified over 3 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

OK

OPERATING SYSTEMS BY LANDON, KYLE, AND ETHAN. WHAT IS THEIR PURPOSE? (1) manage the computer's resources, such as the central processing unit (2) establish.

OPERATING SYSTEMS BY LANDON, KYLE, AND ETHAN. WHAT IS THEIR PURPOSE? (1) manage the computer's resources, such as the central processing unit (2) establish.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on nutrition in human beings Ppt on environment safety measures Ppt on business environment nature concept and significance of study Create ppt on ipad 2 Ppt on zettabyte file system Ppt on seven segment display tutorials Download ppt on school management system Ppt on abstract art ideas Download ppt on water a precious resource Ppt online exam form