Abstract: It is common for many oscillatory systems to encounter incursive fractal boundaries between different attracting domains in their phase spaces due to their complex dynamical behaviors. This study is focused on the global dynamics of a nonlinear oscillator with rigid constraints under multiple harmonic and bounded-noise excitations. The well-known cell mapping method is developed, and a specific Poincare map is then introduced to simulate the global dynamics of the system. It is shown that several kinds of stochastic attractors may coexist in the space of such system by adjusting the parameters’ values. In addition, random fractal boundaries will arise between different attracting domains of stochastic attractors.