AUTO-07P : CONTINUATION AND BIFURCATION SOFTWARE FOR ORDINARY DIFFERENTIAL EQUATIONS Eusebius J. Doedel and Bart E. Oldeman Concordia University Montreal, Canada with major contributions by Alan R. Champneys (Bristol), Fabio Dercole (Milano), Thomas Fairgrieve (Toronto), Yuri Kuznetsov (Utrecht), Randy Paffenroth (Pasadena), Bj¨ornSandstede (Brown), Xianjun Wang, and Chenghai Zhang. January 2012 Contents 1 Installing AUTO. 11 1.1 Installation. 11 1.1.1 Installation on Linux/Unix . 12 1.1.2 Installation on Mac OS X . 13 1.1.3 Installation on Windows . 14 1.2 Restrictions on Problem Size. 15 1.3 Compatibility with Earlier Versions. 15 1.4 Parallel Version. 16 2 Overview of Capabilities. 18 2.1 Summary. 18 2.2 Algebraic Systems. 18 2.3 Ordinary Differential Equations. 19 2.4 Parabolic PDEs. 20 2.5 Discretization. 21 3 User-Supplied Files. 22 3.1 The Equations-File xxx.f90, or xxx.f, or xxx.c . 22 3.2 The Constants-File c.xxx .............................. 22 3.3 User-Supplied Routines. 23 3.4 User-Supplied Derivatives. 23 4 Running AUTO using Python Commands. 25 4.1 Typographical Conventions . 25 4.2 General Overview. 25 4.3 First Example . 26 4.4 Scripting . 30 4.5 Second Example . 30 4.6 Extending the AUTO CLUI . 34 4.7 Bifurcation Diagram Objects . 37 4.7.1 Solutions . 41 4.7.2 Summary and reference . 45 4.8 Importing data from Python or external tools. 46 4.9 Exporting output data for use by Python or external visualization tools. 46 4.10 The .autorc or autorc File . 46 1 4.11 Plotting Tool . 47 4.12 The Plotting Tool PLAUT04 . 50 4.13 Quick Reference . 50 4.14 Reference . 53 4.14.1 Basic commands. 53 4.14.2 Plotting commands. 56 4.14.3 File-manipulation. 56 4.14.4 Diagnostics. 57 4.14.5 File-maintenance. 59 4.14.6 Copying a demo. 63 4.14.7 Python data structure manipulation functions. 63 4.14.8 Shell Commands. 65 5 Running AUTO using Unix Commands. 66 5.1 Basic commands. 66 5.2 Plotting commands. 67 5.3 File-manipulation. 67 5.4 Diagnostics. 68 5.5 File-editing. 70 5.6 File-maintenance. 70 5.7 HomCont commands. 72 5.8 Copying a demo. 72 5.9 Viewing the manual. 72 6 Output Files. 73 7 The Graphics Programs PLAUT and PyPLAUT. 76 7.1 Basic PLAUT-Commands. 76 7.2 Default Options. 77 7.3 Other PLAUT-Commands. 78 7.4 Printing PLAUT Files. 78 8 The Graphics Program PLAUT04. 79 8.1 Quick start . 79 8.1.1 Starting and stopping Plaut04 ....................... 79 8.1.2 Changing the \Type" . 80 8.1.3 Changing the \Style" . 80 8.1.4 Coordinate axes . 80 8.1.5 Options . 80 8.1.6 CR3BP animation . 80 8.1.7 Help . 81 8.1.8 Picking a point in the diagram . 81 8.1.9 Choosing the variables . 83 8.1.10 Choosing labels . 84 8.1.11 Coloring . 84 2 8.1.12 Number of periods to be animated . 84 8.1.13 Changing the line/tube thickness . 85 8.1.14 Changing the animation speed . 85 8.1.15 Changing the background picture . 85 8.2 Setting up the resource file . 85 8.3 Example . 89 9 The Graphical User Interface GUI94. 92 9.1 General Overview. 92 9.1.1 The Menu bar. 92 9.1.2 The Define-Constants-buttons. 92 9.1.3 The Load-Constants-buttons. 93 9.1.4 The Stop- and Exit-buttons. 93 9.2 The Menu Bar. 93 9.2.1 Equations-button. 93 9.2.2 Edit-button. 93 9.2.3 Write-button. 93 9.2.4 Define-button. 93 9.2.5 Run-button. 94 9.2.6 Save-button. 94 9.2.7 Append-button. 94 9.2.8 Plot-button. 94 9.2.9 Files-button. 94 9.2.10 Demos-button. 94 9.2.11 Misc.-button. 95 9.2.12 Help-button. 95 9.3 Using the GUI. 95 9.4 Customizing the GUI. 95 9.4.1 Print-button. 95 9.4.2 GUI colors. 95 9.4.3 On-line help. 96 10 Description of AUTO-Constants. 97 10.1 The AUTO-Constants File. 97 10.2 Problem Constants. 98 10.2.1 NDIM ...................................... 98 10.2.2 NBC ....................................... 98 10.2.3 NINT ...................................... 98 10.2.4 NPAR ...................................... 98 10.2.5 JAC ....................................... 98 10.3 Discretization Constants. 98 10.3.1 NTST ...................................... 98 10.3.2 NCOL ...................................... 99 10.3.3 IAD ....................................... 99 10.4 Tolerances. 99 3 10.4.1 EPSL ...................................... 99 10.4.2 EPSU ...................................... 99 10.4.3 EPSS ...................................... 99 10.4.4 ITMX ...................................... 99 10.4.5 NWTN ...................................... 100 10.4.6 ITNW ...................................... 100 10.5 Continuation Step Size. ..