A Van der Pol oscillator subjected to complicated excitations chaotic phenomenon

Abstract

This paper deals with the Van der Pol oscillator subjected to complicated excitations. Section 1 presents the Van der Pol oscillator with a variable friction force . Section 2 is concerned with a Van der Pol oscillator under a simultaneous influence of forced and nonlinear parametric excitations. Section 3 is devoted to the regular oscillation and chaotic phenomenon in a forced, strongly nonlinear Van der Pol’s oscillator. The stationary oscillations, their stability and transitional regimes and also chaotic phenomenon are of special interest. The asymptotic method of nonlinear mechanics and the method of harmonic balance, in combination with a computer, are used.