Lyapunov Space of Coupled FM Oscillators

Linux Audio Conference 2013 Paper

LAC2013

Abstract

I consider two coupled oscillators, each modulating the other's frequency. This system is governed by four parameters: the base frequency and modulation index for each oscillator. For some parameter values the system becomes unstable. I use the Lyapunov exponent to measure the instability. I generate images of the parameter space, implementing the number crunching on graphics hardware using OpenGL. I link the mouse position over the displayed image to realtime audio output, creating an audio-visual browser for the 4D parameter space.

Download

• 14MB PDF
• 180kB PDF

Linux Audio Conference 2013 Slides

Download

• 6.3MB PDF slides
• 12MB MKV video example zooming and rotating through 4D parameter space
• 590kB Ogg audio excerpt from Soft Rock EP

Author

Claude Heiland-Allen