Constrained Differential Equations as Complex Sound Generators

This paper presents investigations for complex sound generation based on modified classic chaotic differential equations. The modification consists of a constraining structure, a cascaded saturating nonlinearity and DC-blocker unit within the recursive paths of the differential equations. The new configuration allows for the exploration of these equations in unstable regions, increasing the parameters ranges allowed and extending sonic possibilities. Furthermore, the configuration implements a low-level competing mechanism between positive and negative feedback relations that forces oscillation and enhances complex variations both at timbral and formal time scales. The resulting systems exhibit phase spaces with nontrivial trajectories and show potential for computer music and, particularly, applications requiring some degree of autonomy. The sound generators are implemented in the Faust programming language and are published on Github under the GNU GPL v3.0 license