A simple autonomous quasiperiodic self-oscillator

In this note a simple example of an autonomous three-dimensional system is considered demonstrating quasiperiodic dynamics because of presence of two coexisting oscillatory components of independently controlling and, hence, generally incommensurate frequencies. Attractor in such a regime is a two-dimensional torus. Numerical illustrations of the stable quasiperiodic motions are presented. Some essential features of the dynamical behavior are revealed: in particular, charts of dynamical regimes on parameter planes are considered and discussed. (C) 2009 Elsevier B.V. All rights reserved.