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AUTO-07P : CONTINUATION AND
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AUTO-07P : CONTINUATION AND
Contents
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
commandCat
commandCd
commandClean
commandCopyAndLoadDemo
commandCopyDataFiles
commandCopyDemo
commandCopyFortFiles
commandCreateGUI
commandDeleteDataFiles
commandDeleteFortFiles
commandDouble
commandInteractiveHelp
commandLs
commandMoveFiles
commandParseConstantsFile
commandParseDiagramAndSolutionFile
commandParseDiagramFile
commandParseSolutionFile
commandPlotter
commandPlotter3D
commandQueryBranchPoint
commandQueryEigenvalue
commandQueryFloquet
commandQueryHopf
commandQueryIterations
commandQueryLimitpoint
commandQueryNote
commandQuerySecondaryPeriod
commandQueryStepsize
commandRun
commandRunnerConfigFort2
commandRunnerConfigFort12
commandRunnerLoadName
commandRunnerPrintFort2
commandRunnerPrintFort12
commandShell
commandSpecialPointLabels
commandTriple
commandUserData
commandWait
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
Starting and stopping PLAUT04
Changing the ``Type''
Changing the ``Style''
Coordinate axes
Options
CR3BP animation
Help
Picking a point in the diagram
Choosing the variables
Choosing labels
Coloring
Number of periods to be animated
Changing the line/tube thickness
Changing the animation speed
Changing the background picture
Setting up the resource file
Example
The Graphical User Interface GUI94.
General Overview.
The Menu bar.
The Define-Constants-buttons.
The Load-Constants-buttons.
The Stop- and Exit-buttons.
The Menu Bar.
Equations-button.
Edit-button.
Write-button.
Define-button.
Run-button.
Save-button.
Append-button.
Plot-button.
Files-button.
Demos-button.
Misc.-button.
Help-button.
Using the GUI.
Customizing the GUI.
Print-button.
GUI colors.
On-line help.
Description of AUTO-Constants.
The AUTO-Constants File.
Problem Constants.
NDIM
NBC
NINT
JAC
Discretization Constants.
NTST
NCOL
IAD
Tolerances.
EPSL
EPSU
EPSS
ITMX
NWTN
ITNW
Continuation Step Size.
DS
DSMIN
DSMAX
IADS
NTHL
NTHU
Diagram Limits.
NMX
RL0
RL1
A0
A1
Free Parameters.
NICP, ICP
Fixed points.
Periodic solutions and rotations.
Folds and Hopf bifurcations.
Folds and period-doublings.
Boundary value problems.
Boundary value folds.
Optimization problems.
Internal free parameters.
Parameter overspecification.
Computation Constants.
ILP
ISP
ISW
MXBF
IRS
IPS
Output Control.
NPR
IID
IPLT
NUZR
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 B 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.
NUNSTAB
NSTAB
IEQUIB
ITWIST
ISTART
NREV, IREV
NFIXED, IFIXED
NPSI, IPSI
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
truein
Subsections
Preface
Acknowledgments
License
Gabriel Lord 2007-11-19