On transitions between quasilinear and relaxational regimes in self-oscillators

The Lienard (Rayleigh) equation for a self-oscillator with a number of limit cycles at small values of the dissipative parameter, mu >0, is considered for all values of mu epsilon (0, infinity ). It is shown that essential qualitative changes in the structure of the phase plane can occur at intermediate values of mu , between quasilinear and relaxational regimes of oscillation. The illustration of such events and the classification of topologically conjugate equivalence classes of dynamical systems are given along with some numerical examples.<>