Thursday, July 17, 2014

Chaotic Behavior and Shil’nikov Homoclinic Orbits

My exploration of chaos continues...equation (5) from Sprott's paper:

dx/dt = -y - z

dy/dt = x

dz/dt = a(y - y2) - bz , with a = b = 0.5.

This was interesting because the first attempt ended in failure (i.e. overload condition on all the amplifiers); a bit of sleuthing uncovered a typo in equation (5) for the dz/dt term (the final x should, in fact, be a z)...and voila...
It is the Rössler prototype-4 system, apparently. The picture below shows how I figured out the patching (I have taught myself to mark up each connection on the diagram with a highlighter pen, as I patch that lead physically on the computer...this avoids my getting into a complete mess...). Also, you can see the crossed out part of the first, wrong, attempt...




No comments:

Post a Comment