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

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