On the nonlinear stochastic dynamics of an Atomic Force Microscope cantilever

Abstract Atomic Force Microscopy (AFM) serves characterization and actuation in nanoscale applications. We study the stochastic dynamics of an AFM cantilever under tip-sample interactions represented by the Lennard–Jones and Morse potential energy functions. In both cases, we also study the contrasting dynamic effects of additive (external) and multiplicative (internal) noise. Moreover, for multiplicative noise, we study the two sub-cases arising from the Ito and Stratonovich interpretations of stochastic integrals. In each case, we also investigate stochastic stability of the system by tracing the time evolution of the maximal Lyapunov exponent. Additionally, we obtain stationary probability densities for the unforced dynamics using stochastic averaging.