How to build a MATLAB demonstrator solving dynamical systems in real-time, with audio output and MIDI control

Abstract

This paper explains and provides code to synthesize and control, in real-time, the audio signals produced by a dynamical system. The code uses only the Matlab programming language. It can be controlled with an external MIDI (Musical Instrument Data Interface) device, such as a MIDI keyboard or wind controller, or with mouse-operated sliders. In addition to the audio output, the demonstrator computes and displays the amplitude and fundamental frequency of the signal, which is useful to quantify the dynamics of the model. For the sake of this example, it is a type of Van der Pol oscillator, but more complex systems can be handled. The demonstrator holds potential for pedagogical and preliminary research applications, for various topics related to dynamical systems: direct and inverse bifurcations, transient effects such as dynamical bifurcations, artifacts introduced by integration schemes, and above all, the dynamics of self-sustained musical instruments.