Equation-free bifurcation analysis of a stochastically excited Duffing oscillator

In this paper, an extensive analysis of a stochastically excited one-degree-of-freedom mechanical system with cubic nonlinearity is presented. This motivated by the need for realistic bifurcation analyses stochastic dynamical systems, given that many physical applications contain significant time-varying uncertainty can lead to drastically different solutions from deterministic case. The proposed methodology based on pseudo arc-length continuation combined moment-map method, which allows investigation systems behaviour. It shown introduction noise in excitation leads destabilisation stable periodic orbits over time underlying system. For better interpretation and lower computational costs, instead continuation, diagram modified detection approximation mean first passage introducing three methods. Two semi-analytical approaches Markov models, together completely numerical method time, are compared each other similar results. parameter sensitivity comparison methods support structural dynamic cases.