Stochastic pitchfork bifurcation: Numerical simulations and symbolic calculations using MAPLE (Q1897675)

This paper presents results of simulations done to study pitchfork bifurcation of the nonlinear stochastic differential equation \[ dx_t = (\alpha x + \beta x^3)dt + \sigma_1 x dw^1_t + \sigma_2 x^3 dw^2_t \] where \((w^1_t, w^2_t)\) is a Wiener process taking values in \(\mathbb{R}^2\). An example is given of using MAPLE to transform a noisy van de Pol-Duffing oscillator into a normal form conducive to the identification of pitchfork bifurcation.