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 propos...

The cubic spline interpolation method, the Runge–Kutta method, and the Newton–Raphson method are extended to dual versions (developed in the context of dual numbers). This extension allows the calculation of the derivatives of complicated compositions of functions which are not necessarily defined by a closed form expression. The code for the algorithms has been written in Fortran and some exam...