- Materials Simulation Group
- Navigation Menu
- About me
- Gus Hart's Physics Page
- Curriculum Vita
- Publications
- Schedule
- BYU Handball Club
- Classes
- Physics 123
- Physics of Life (313R)
- Biophysics
- Research opportunities for students
- Materials Simulation Group
- MSG Wiki
- Computation
- BYU Supercomputing
- Matlab tutorial (NAU)
- Matlab tutorial (BYU)
- Matlab & Chaos
- Crystal structures
- NRL Database
- ISODISPLACE
- Handball
- BYU Handball Club
- World Pro Handball
- USU Handball PE class
- Bike vs. Chapman Snippet
- Women's 2007 Champ Snippet
- US Handball Assoc.
- What is it? (3 min. video)
- Useful bits
- Gardner notes
- Compiling
- Miscellaneous
- What is BYU all about?
- Yes, I'm a Mormon (LDS)

- Navigation Menu
- Department Menu
- Department Directory

Matlab has some nice built-in functions for solving differential equations numerically and can do animations quite easily, so it's a handy way to explore chaotic systems (that can be represented by non-linear differential equations) without doing a whole lot of programming.

Here are some examples of using Matlab built-in "integrators".

- decay.m A simple "decay" model; first-order, linear ordinary differential equation.
- sho.m & sho_2.m Just a simple harmonic oscillator. (The second one has adjustable parameters for the spring constant and the mass.)

The physical system modeled here is a mass attached to an ideal spring which oscillates back and forth along the x-axis without friction. - pendulum.m A simple pendulum. Nearly the same as above except the restoring force is propotional to the sine of the displacement rather than just the displacement. This makes the system non-linear (but not chaotic...yet)
- ddp.m A damped, driven pendulum. A pendulum where friction has been added (as a velocity-dependent term) and a periodic driving force keeps adding energy to the system. For some parameter ranges this system is chaotic. This one takes ~30 seconds to make the second plot (a Poincare plot--try zooming in!).
- plr.m A simple sytem described as a "piece-wise, linear, Roessler-like oscillator". It's only non-linear because of the piecewise-defined driving term in the third equation---yet, this is sufficient to make it chaotic. The three coupled equations model a simple, chaoticc electric circuit. See PRL
**96**244102 (2006).

Contact Gus Hart
with questions or comments about this site.

Copyright © Brigham Young University Department of Physics & Astronomy. All Rights Reserved.

Copyright © Brigham Young University Department of Physics & Astronomy. All Rights Reserved.