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When the vibrating microcantilever in an atomic force microscope (AFM) is close to the sample surface, the nonlinear tip-sample interaction will greatly influence the dynamics of the cantilever. In this paper, the effect of the bounded noise parametric excitation on the nonlinear dynamic behavior of dynamic AFM system is investigated. The microcantilever is modeled by a single-lumped-mode approximation and the interactions between the microcantilever and sample are described by the Lennard-Jones (LJ) potential. Numerical simulations are carried out to study the coupled nonlinear dynamic system in terms of bifurcation diagram, Poincaré maps, largest Lyapunov exponent, phase portraits, and time histories in detail. Effects of the density of the random disturbance with bounded noise, material property, and contact angle of the meniscus force are analyzed and discussed. The results indicate that periodic and chaotic motions occur in the dynamic AFM system. It is demonstrated that the coupled dynamic system goes through a complex nonlinear behavior as the system parameters change and the effect of bounded noise cannot be ignored in the further design of an AFM.