Regular and chaotic vibrations of van der Pol-Mathieu oscillator with non-ideal energy source

Vibrations of a parametrically and self-excited system with a non-ideal source of energy have been analysed in this paper. The model has consisted of the van der Pol-Mathieu oscillator and non-ideal energy source, which characteristic has been assumed as a straight line. Regular motion of the complete system, energy source – vibrating model, near the main parametric resonance, has been solved analytically by the applying Krilov-Bogolubov-Mitropolski method. Possible types of motion and transition from regular to chaotic motion have been investigated by using the Lyapunov's exponent criterion and attractor topological structure analysis.