Erosion of safe basins in a nonlinear oscillator under bounded noise excitation

The erosion of the safe basins of a quadratic nonlinearity oscillator under harmonic or bounded random noise excitations is studied in detail by the Monte-Carlo method. It is found that a small random disturbance may destroy the integrity of the safe basins, thus making the system less safe. However, numerical results show that increasing the systemʹs damping and decreasing the systemʹs nonlinearity may enlarge the original integral safe basins. As an alternative definition, stochastic bifurcation may be defined as a sudden change in the character of stochastic safe basins when the bifurcation parameter of the system passes through a critical value, which is different from the previous ones by the authors, where stochastic bifurcation may be defined as a sudden change in the character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value.