On Dynamical Behavior of Atomic Force Microscopy: A Short Review

Atomic force microscopy is an experimental analysis widely used in recent years to determine the topology of biological and synthetic samples. This experimental analysis has been widely applied because it is not a destructive technique, that is, there is no destruction of the samples to be analyzed. Due to this wide applicability, we explore a mini-review of two systems in a mathematical way to determine the behavior of nonlinear dynamics (Lyapunov exponent, Bifurcation Diagrams, and phase portraits) and of basins of attraction. Such results corroborate the literature and allow establishing the parameters in which the nonlinear dynamics is in a chaotic or periodic regime, thus opening possibilities for the application of techniques that can suppress chaos and thus determine more accurate images of the analyzed samples.