Bifurcation and chaos of atomic-force-microscope probes driven in Lennard-Jones potentials

Bifurcation and chaos in atomic force microscope are investigated. The one-term and two-term Galerkin truncations are, respectively, employed to simplify the partial-differential equation that governs the motions of the microcantilever to a set of ordinary differential equations. By use of Poincare maps, the dynamical behaviors are identified based on the numerical solutions of the governing equations. Bifurcation diagrams are presented in the case that the excitation amplitude increases while other parameters are fixed. Numerical simulations indicate that periodic and chaotic motions occur in the system and one-term truncation and two-term truncation give the qualitatively same results.