The atomic force microscope (AFM) system has evolved into a useful tool for direct measurements of intermolecular forces with atomic-resolution characterization that can be employed in a broad spectrum of applications. In this paper, the nonlinear dynamical behavior of the AFM is studied. This is achieved by modeling the microcantilever as a single mode approximation (lumped-parameters model) and considering the interaction between the sample and cantilever in the form of van der Waals potential. The resultant nonlinear system is then analyzed using Melnikov method, which predicts the regions in which only periodic and quasi-periodic motions exist, and also predicts the regions that chaotic motion is possible. Numerical simulations are used to verify the presence of such chaotic invariant sets determined by Melnikov theory. Finally, the amplitude of vibration in which chaos is appeared is investigated and such irregular motion is proven by several methods including Poincare maps, Fourier transform, autocorrelation function and Lyapunov exponents.

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