Contents

• Installing AUTO.
  • Installation.
  • Restrictions on Problem Size.
  • Compatibility with Older Versions.
• Overview of Capabilities.
  • Summary.
  • Algebraic Systems.
  • Ordinary Differential Equations.
  • Parabolic PDEs.
  • Discretization.
• How to Run AUTO.
  • User-Supplied Files.
    • The equations-file xxx.f
    • The constants-file r.xxx
  • User-Supplied Subroutines.
  • Arguments of STPNT.
  • User-Supplied Derivatives.
  • Running AUTO using Command Mode.
    • Basic commands.
    • Plotting commands.
    • File-manipulation.
    • Diagnostics.
    • File-editing.
    • File-maintenance.
    • HomCont commands.
    • Copying a demo.
    • Pendula animation.
    • Viewing the manual.
  • Output Files.
• The Graphics Program PLAUT.
  • Basic PLAUT-Commands.
  • Default Options.
  • Other PLAUT-Commands.
  • Printing PLAUT Files.
• Graphical User Interface.
  • 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
• 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.
  • ab : A Tutorial Demo.
  • Copying the Demo Files.
  • Executing all Runs Automatically.
  • Executing Selected Runs Automatically.
  • Using AUTO-Commands.
  • Plotting the Results with PLAUT.
  • Following Folds and Hopf Bifurcations.
  • Relabeling Solutions in the Data-Files.
  • Plotting the 2-Parameter Diagram.
  • Converting Saved PLAUT Files to PostScript.
  • Using the GUI.
  • Abbreviated AUTO-Commands.
• 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 : Period-Doubling Continuation.
  • 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 Subroutine PVLS.
  • ext : Spurious Solutions to BVP.
  • tim : A Test Problem for Timing AUTO.
• HomCont.
  • Introduction.
  • HomCont Files and Subroutines.
  • 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.
• References
• About this document ...

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