The field of nonlinear dynamics deals with mathematical techniques to study the nonlinear equations that serve as models of physical systems. The benefits of using nonlinear dynamics concepts to interpret and predict probe oscillations in dynamic AFM  are becoming increasingly clear. Nonlinear dynamics lies at the heart of probe instabilities , tip-sample dissipation processes , and higher harmonic generation in AFM .
In this talk we will first review known experimental phenomena in dynamic AFM, and how a nonlinear dynamicist interprets them. We will then discuss recent experimental results that have established the existence of chaos in tapping mode AFM under reasonable operating conditions [5, 6]. We will also discuss parametric resonance, a phenomenon that underlies the physics of surface waves and of childrens swings, and its recent implementation in dynamic AFM . While still in its infancy, this is a completely different way of oscillating an AFM probe that offers significant promise while posing specific challenges.
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