Controllable branching of robust response patterns in nonlinear mechanical resonators

In lieu of continuous time active feedback control in complex systems, nonlinear dynamics offers a means to generate desired long-term responses using short-time control signals. This type of control has been proposed for use in resonators that exhibit a plethora of complex dynamic behaviors resulting from energy exchange between modes. However, the dynamic response and, ultimately, the ability to control the response of these systems remains poorly understood. Here, we show that a micromechanical resonator can generate diverse, robust dynamical responses that occur on a timescale five orders of magnitude larger than the external harmonic driving and these responses can be selected by inserting small pulses at specific branching points. We develop a theoretical model and experimentally show the ability to control these response patterns. Hence, these mechanical resonators may represent a simple physical platform for the development of springboard concepts for nonlinear, flexible, yet robust dynamics found in other areas of physics, chemistry, and biology.

Automated summary

In contrast to continuous time active feedback control in complex systems, nonlinear dynamics provides a method to generate desired long-term responses using short-time control signals. We demonstrate that a micromechanical resonator can produce diverse, robust dynamical responses on a timescale much larger than the external harmonic driving, and these responses can be selectively controlled by inserting small pulses at specific branching points. We develop a theoretical model and experimentally confirm the ability to control these response patterns. Therefore, these mechanical resonators may serve as a simple physical platform for investigating the nonlinear, flexible, and robust dynamics observed in other fields such as physics, chemistry, and biology.