Iterated maps for clarinet-like systems

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.)

Comparison of the bifurcation scenarios predicted by the single-mode and multimode semiconductor laser rate equations

We present a detailed comparison of the bifurcation scenarios predicted by single-mode and multimode semiconductor laser rate equation models under large amplitude injection current modulation. The influence of the gain model on the predicted dynamics is investigated. Calculations of the dependence of the time averaged longitudinal mode intensities on modulation frequency are compared with experiments performed on an AlxGa1-xAs Fabry-Pérot semiconductor laser.K. A. Corbett and M. W. Hamilto

Roughening Interfaces in Deterministic Dynamics

Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface. I. INTRODUCTION Dynamics of growing and roughening interfaces have been intensively investigated recently[1]. This phenomenon is of importance in deposition, crystal growth, two-phase flow in porous media, etc. The universal equation governing the motion of the interface was derived by Kardar, Parisi and Zhang (KPZ)[2]: @H @t = 2 ( @H ..

Modeling Qualitative Changes in Bimanual Movements

this paper we present an iterated map model to explain main findings of these experiments. The model consists of two iterated maps describing the dynamics of the finger movements. The essential properties of the model are a nonlinear correction function and a coupling mechanism between the two maps. Numerical simulations show that the model is in qualitative agreement with the experimentally observed phenomena. I. INTRODUCTIO