Tools and Scripts

acf.pl A Perl script that builds an AUTO constants file based on input from the user. Very simplistic, but useful for getting started. (Last update: 18 June 2003)

Miscellaneous Matlab Files

pulse1.m A Matlab function that creates periodic pulses with a given "width" and amplitude 1.
pulse2.m A Matlab function that creates periodic pulses with a given "width" and area 1.
pulse3.m A Matlab function that creates periodic pulses with a given "width" and period, and with height 1.
pulse4.m A Matlab function that creates periodic pulses with a given "width" and period, and with area 1.
smoothstep.m smoothstep(t) returns: 0 if t < 0; 1 if t > 1; and p(t) if 0 < t < 1, where p(t) is a polynomial that smoothly connects 0 to 1. All derivatives up to and including the fourth are zero at t=0 and t=1.

AUTO 2000 Examples and Applications

  1. Forced, Damped Linear Oscillator. The following files are used to create a damped resonance plot for a forced, damped, linear oscillator. (See, for example, Boyce and DiPrima (7th ed), Figure 3.9.3, or Blanchard, Devaney and Hall (2nd ed), Figure 4.22.) In the equations file flin2.c, a variable θ=ωt is used (so the differential equation for θ is simply θ′=ω). In one period of the solution, θ increases by 2π. AUTO detects this and deduces that θ is a "rotation".
    flin2.c The AUTO equations file for a forced linear system.
    c.flin2 The AUTO constants file.
    flin2.dat A data file created by the MATLAB script flscript2.m The four columns are t, x, y, theta. The parameters were omega=1, a=1, b=2, and k=10.
    res2.auto An AUTO script (written using the "CLUI" commands) to generate the resonance plot. Run it by entering the command auto res2.auto in a Unix shell.
    flscript2.m A MATLAB script that creates a periodic orbit data file to be used as a starting point in AUTO
    flinsys.m The MATLAB version of the differential equations for the forced linear system. (This function is used by flscript2.m.)
    flin2.tar tar file containing all the above files.

  2. Forced, damped linear oscillator (another version). The following files are also used to create a resonance plot for the forced, damped linear oscillator. In this version, the periodic forcing is handled using the same method as in the "frc" AUTO demo.
    flin.c The AUTO equations file for a forced linear system.
    c.flin The AUTO constants file.
    flin.dat A data file created by the MATLAB script flscript.m (omega=1, b=2, k=10).
    res.auto An AUTO script (written using the "CLUI" commands) to generate the resonance plot.
    flscript.m A MATLAB script that creates a periodic orbit data file to be used as a starting point in AUTO
    flinsys.m The MATLAB version of the differential equations for the forced linear system. (This function is used by flscript.m.)
    flin.tar.gz gzip'd tar file containing all the above files.

  3. Forced weakly nonlinear oscillator. This example is similar to the first example above, but the system being forced is a weakly nonlinear oscillator.
    wn.c The AUTO equations file.
    c.wn The AUTO constants file.
    wn.dat A data file created by the MATLAB script wnscript.m.
    wn.auto An AUTO script (written using the "CLUI" commands) to generate the resonance plot.
    wnscript.m A MATLAB script that creates a periodic orbit data file to be used as a starting point in AUTO.
    wnsys.m The MATLAB version of the differential equations of the forced weakly nonlinear oscillator. (This function is used by wnscript.m.)
    wn.tar tar file containing all the above files.