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AUTO-07P :
CONTINUATION AND BIFURCATION SOFTWARE
FOR ORDINARY DIFFERENTIAL EQUATIONS

Eusebius J. Doedel
Concordia University
Montreal, Canada

with major contributions by

Alan R. Champneys (Bristol), Thomas Fairgrieve (Toronto),
Yuri Kuznetsov (Utrecht), Bart Oldeman, Randy Paffenroth (Pasadena),
Björn Sandstede (Surrey), Xianjun Wang, and Chenghai Zhang.

Date: August 2007

Contents
- Preface
- Acknowledgments
- License
Installing AUTO.
- Installation.
  - Installation on Mac OS X
  - Installation on Windows
- Restrictions on Problem Size.
- Compatibility with Earlier Versions.
- Parallel Version.
Overview of Capabilities.
- Summary.
- Algebraic Systems.
- Ordinary Differential Equations.
- Parabolic PDEs.
- Discretization.
User-Supplied Files.
- The Equations-File xxx.f90, or xxx.f, or xxx.c
- The Constants-File c.xxx
- User-Supplied Routines.
- User-Supplied Derivatives.
Running AUTO using Python Commands.
- Typographical Conventions
- General Overview.
- First Example
- Scripting
- Second Example
- Extending the AUTO CLUI
- Bifurcation Diagram Files
- Solution Files
- Exporting output data for use by Python or external visualization tools.
- The .autorc File
- Two Dimensional Plotting Tool
- Three Dimensional Plotting Tool
- Quick Reference
- Reference
  - commandAppend
- Purpose
- Description
- Aliases
  - commandCat
- Purpose
- Description
- Aliases
  - commandCd
- Purpose
- Description
- Aliases
  - commandClean
- Purpose
- Description
- Aliases
  - commandCopyAndLoadDemo
- Purpose
- Description
- Aliases
  - commandCopyDataFiles
- Purpose
- Description
- Aliases
  - commandCopyDemo
- Purpose
- Description
- Aliases
  - commandCopyFortFiles
- Purpose
- Description
- Aliases
  - commandCreateGUI
- Purpose
- Description
- Aliases
  - commandDeleteDataFiles
- Purpose
- Description
- Aliases
  - commandDeleteFortFiles
- Purpose
- Description
- Aliases
  - commandDouble
- Purpose
- Description
- Aliases
  - commandInteractiveHelp
- Purpose
- Description
- Aliases
  - commandLs
- Purpose
- Description
- Aliases
  - commandMoveFiles
- Purpose
- Description
- Aliases
  - commandParseConstantsFile
- Purpose
- Description
- Aliases
  - commandParseDiagramAndSolutionFile
- Purpose
- Description
- Aliases
  - commandParseDiagramFile
- Purpose
- Description
- Aliases
  - commandParseSolutionFile
- Purpose
- Description
- Aliases
  - commandPlotter
- Purpose
- Description
- Aliases
  - commandPlotter3D
- Purpose
- Description
- Aliases
  - commandQueryBranchPoint
- Purpose
- Description
- Aliases
  - commandQueryEigenvalue
- Purpose
- Description
- Aliases
  - commandQueryFloquet
- Purpose
- Description
- Aliases
  - commandQueryHopf
- Purpose
- Description
- Aliases
  - commandQueryIterations
- Purpose
- Description
- Aliases
  - commandQueryLimitpoint
- Purpose
- Description
- Aliases
  - commandQueryNote
- Purpose
- Description
- Aliases
  - commandQuerySecondaryPeriod
- Purpose
- Description
- Aliases
  - commandQueryStepsize
- Purpose
- Description
- Aliases
  - commandRun
- Purpose
- Description
- Aliases
  - commandRunnerConfigFort2
- Purpose
- Description
- Aliases
  - commandRunnerConfigFort12
- Purpose
- Description
- Aliases
  - commandRunnerLoadName
- Purpose
- Description
- Aliases
  - commandRunnerPrintFort2
- Purpose
- Description
- Aliases
  - commandRunnerPrintFort12
- Purpose
- Description
- Aliases
  - commandShell
- Purpose
- Description
- Aliases
  - commandSpecialPointLabels
- Purpose
- Description
- Aliases
  - commandTriple
- Purpose
- Description
- Aliases
  - commandUserData
- Purpose
- Description
- Aliases
  - commandWait
- Purpose
- Description
- Aliases
Running AUTO using Unix Commands.
- Basic commands.
- Plotting commands.
- File-manipulation.
- Diagnostics.
- File-editing.
- File-maintenance.
- HomCont commands.
- Copying a demo.
- Viewing the manual.
Output Files.
The Graphics Program PLAUT.
- Basic PLAUT-Commands.
- Default Options.
- Other PLAUT-Commands.
- Printing PLAUT Files.
The Graphics Program PLAUT04.
- Quick start
- Setting up the resource file
- Example
The Graphical User Interface GUI94.
- General Overview.
- The Menu Bar.
- Using the GUI.
- Customizing the GUI.
Description of AUTO-Constants.
- The AUTO-Constants File.
- Problem Constants.
- Discretization Constants.
- Tolerances.
- Continuation Step Size.
- Diagram Limits.
- Free Parameters.
- Computation Constants.
- Output Control.
- Quick reference
Notes on Using AUTO.
- Restrictions on the Use of PAR.
- Efficiency.
- Correctness of Results.
- Bifurcation Points and Folds.
- Floquet Multipliers.
- Memory Requirements.
AUTO Demos : Tutorial.
- Introduction.
- cusp : A Tutorial Demo.
- Copying the Demo Files.
- Executing all Runs Automatically.
- Plotting the Results with AUTO .
- Plotting the Results with AUTO in 3D.
- Exporting the Results for different plotters.
- ab : A Programmed Demo.
AUTO Demos : Fixed points.
- enz : Stationary Solutions of an Enzyme Model.
- dd2 : Fixed Points of a Discrete Dynamical System.
AUTO Demos : Periodic solutions.
- lrz : The Lorenz Equations.
- abc : The A $\to$ B $\to$ C Reaction.
- pp2 : A 2D Predator-Prey Model.
- lor : Starting an Orbit from Numerical Data.
- frc : A Periodically Forced System.
- ppp : Continuation of Hopf Bifurcations.
- plp : Fold Continuation for Periodic Solutions.
- pp3 : Periodic Families and Loci of Hopf Points.
- tor : Detection of Torus Bifurcations.
- pen : Rotations of Coupled Pendula.
- chu : A Non-Smooth System (Chua's Circuit).
- phs : Effect of the Phase Condition.
- ivp : Time Integration with Euler's Method.
AUTO Demos : BVP.
- exp : Bratu's Equation.
- int : Boundary and Integral Constraints.
- bvp : A Nonlinear ODE Eigenvalue Problem.
- lin : A Linear ODE Eigenvalue Problem.
- non : A Non-Autonomous BVP.
- kar : The Von Karman Swirling Flows.
- spb : A Singularly-Perturbed BVP.
- ezp : Complex Bifurcation in a BVP.
AUTO Demos : Parabolic PDEs.
- pd1 : Stationary States (1D Problem).
- pd2 : Stationary States (2D Problem).
- wav : Periodic Waves.
- brc : Chebyshev Collocation in Space.
- brf : Finite Differences in Space.
- bru : Euler Time Integration (the Brusselator).
AUTO Demos : Optimization.
- opt : A Model Algebraic Optimization Problem.
- ops : Optimization of Periodic Solutions.
- obv : Optimization for a BVP.
AUTO Demos : Connecting orbits.
- fsh : A Saddle-Node Connection.
- nag : A Saddle-Saddle Connection.
- stw : Continuation of Sharp Traveling Waves.
AUTO Demos : Miscellaneous.
- pvl : Use of the Routine PVLS.
- ext : Spurious Solutions to BVB.
- tim : A Test Problem for Timing AUTO .
HomCont.
- Introduction.
- HomCont Files and Routines.
- HomCont-Constants.
- Restrictions on HomCont Constants.
- Restrictions on the Use of PAR.
- Test Functions.
- Starting Strategies.
- Notes on Running HomCont Demos.
HomCont Demo : san.
- Sandstede's Model.
- Inclination Flip.
- Non-orientable Resonant Eigenvalues.
- Orbit Flip.
- Detailed AUTO -Commands.
HomCont Demo : mtn.
- A Predator-Prey Model with Immigration.
- Continuation of Central Saddle-Node Homoclinics.
- Switching between Saddle-Node and Saddle Homoclinic Orbits.
- Three-Parameter Continuation.
- Detailed AUTO -Commands.
HomCont Demo : kpr.
- Koper's Extended Van der Pol Model.
- The Primary Branch of Homoclinics.
- More Accuracy and Saddle-Node Homoclinic Orbits.
- Three-Parameter Continuation.
- Detailed AUTO -Commands.
HomCont Demo : cir.
- Electronic Circuit of Freire et al.
- Detailed AUTO -Commands.
HomCont Demo : she.
- A Heteroclinic Example.
- Detailed AUTO -Commands.
HomCont Demo : rev.
- A Reversible System.
- An -Reversible Homoclinic Solution.
- An -Reversible Homoclinic Solution.
- Detailed AUTO -Commands.
HomCont Demo : Homoclinic branch switching.
- Branch switching at an inclination flip in Sandstede's model.
- Branch switching for a Shil'nikov type homoclinic orbit in the FitzHugh-Nagumo equations.
- Branch switching to a 3-homoclinic orbit in a
  5th-order Korteweg-De Vries model
Bibliography
About this document ...

Gabriel Lord 2007-11-19