Bifurcation analysis of a stochastically excited vibro-impact Duffing-Van der Pol oscillator with bilateral rigid barriers

Abstract

This study focuses on the bifurcation analysis of a Duffing-Van der Pol (DVDP) oscillator with rigid barriers, subjected to additive white noise excitations. This involves mapping the non-smooth vibro-impact system on a continuous phase plane through non-smooth variable transformations. The formulation considers the general case of asymmetrically positioned both sided rigid barriers. The probabilistic description of the system dynamics is subsequently defined through the corresponding Fokker-Planck (FP) equation. The stationary probability density function of the response is numerically obtained by solving the FP equation using finite element method. The stochastic stability of the vibro-impact DVPD oscillator is examined both in terms of D- and P-bifurcations.