Intermittency in amplitude modulated dynamic atomic force microscopy

From a mathematical point of view, the atomic force microscope (AFM) belongs to a special class of continuous time dynamical systems with intermittent impact collisions. Discontinuities of the velocity result from the collisions of the tip with the surface. Transition to chaos in non-linear systems can occur via the following four routes: bifurcation cascade, crisis, quasi-periodicity, and intermittency. For the AFM period doubling and period-adding cascades are well established. Other routes into chaos, however, also may play an important role. Time series data of a dynamic AFM experiment indicates a chaotic mode that is related to the intermittency route into chaos. The observed intermittency is characterized as a type III intermittency. Understanding the dynamics of the system will help improve the overall system performance by keeping the operation parameters of dynamic AFM in a range, where chaos can be avoided or at least controlled.