Iterated maps for clarinet-like systems

Details Iterated maps for clarinet-like systems Iterated maps for clarinet-like systems

2009-12-12

arxiv.org/abs/0912.2439v3

Nonlinear Dynamics 62 (2010) 253-271

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1007/s11071-010-9715-5

The dynamical equations of clarinet-like systems are known to be reducible to a non-linear iterated map within reasonable approximations. This leads to time oscillations that are represented by square signals, analogous to the Raman regime for string instruments. In this article, we study in more detail the properties of the corresponding non-linear iterations, with emphasis on the geometrical constructions that can be used to classify the various solutions (for instance with or without reed beating) as well as on the periodicity windows that occur within the chaotic region. In particular, we find a regime where period tripling occurs and examine the conditions for intermittency. We also show that, while the direct observation of the iteration function does not reveal much on the oscillation regime of the instrument, the graph of the high order iterates directly gives visible information on the oscillation regime (characterization of the number of period doubligs, chaotic behaviour, etc.).

Affiliated with

Also associated with

No associations

Rating

Iterated maps for clarinet-like systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Iterated maps for clarinet-like systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Iterated maps for clarinet-like systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-533380