Real-time demonstrators to exhibit, investigate and teach transient behaviors in nonlinear dynamics, focused on musical instruments

Le résumé fourni par la source

Nonlinear dynamical systems exhibit various transient behaviors, whose understanding is required to fully apprehend how the system responds to sollicitations.This work focuses on multistable systems, where several stable solutions coexist for a given value of the system's parameters.In these settings, transients condition which solution actually appears during time integration.Then, a comprehensive description of the system's behavior entails mapping out the infinite possibilities of variations of the system's parameters with respect to time.This is impractical for models whose phase space is of high dimension, or in limited timescales such as practical activities for students.This work proposes real-time demonstrators of dynamical systems as a way to still investigate these phenomena.The construction of such demonstrators is detailed, including a display outlining the zones of stability of the solutions, and control inputs mimicking a musical instrument (such as a MIDI controller).We show how these elements coupled with audio and visual feedback enables users to quickly gauge a large variety of transient behaviors, for academic proofs of concept or pedagogical activities.A demonstrator for a Van der Pol toy model and one for a woodwind model used for a lab in a master's degree are used as examples.

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