Stable Limit Cycles as Tunable Signal Sources

Wolfram E. Weingartner
DAFx-2025 - Ancona
This paper presents a method for synthesizing audio signals from nonlinear dynamical systems exhibiting stable limit cycles, with control over frequency and amplitude independent of changes to the system’s internal parameters. Using the van der Pol oscillator and the Brusselator as case studies, it is demonstrated how parameters are decoupled from frequency and amplitude by rescaling the angular frequency and normalizing amplitude extrema. Practical implementation considerations are discussed, as are the limits and challenges of this approach. The method’s validity is evaluated experimentally and synthesis examples show the application of tunable nonlinear oscillators in sound design, including the generation of transients in FM synthesis by means of a van der Pol oscillator and a Supersaw oscillator bank based on the Brusselator.
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