The self-oscillating system with compensated dissipation - the dynamics of the approximate discrete map

摘要

We study the van der Pol oscillator subject to an external forcing given by <5-pulses depending on the dynamical variable. In order to simplify the computations, an approximate map is derived by solving the equations between subsequent pulses. It is shown that the period-doubling cascade in this map with nonlinear dissipation converges to a critical point of Hamiltonian type with scaling properties which are known for conservative systems.