Evidence of a nanomechanical resonator being driven into chaotic response via the Ruelle–Takens route

Nanomechanical resonators, of importance for signal filtering and transduction, are investigated within the limit of extreme nonlinear excitation. The Ruelle–Takens route establishes the transition of a system into chaos with n frequencies present. By providing a set of three sources, this transition from linear to nonlinear and finally to chaotic response can be traced, and it is found in our experiment. Knowledge of potentially chaotic behavior of nanomechanical systems is crucial for their application. Our resonator system has an overall length of 4 μm and a cross section of about $\text{100\hspace{0.17em}}\mathrm{nm}\text{×300\hspace{0.17em}}\mathrm{nm}$ with natural frequencies of ∼50 MHz.