Controllable branching of robust response patterns in nonlinear mechanical resonators

Abstract In lieu of active feedback control in complex systems over long timeframes, nonlinear dynamics offers solutions to generate long-term responses. 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. This mechanical system and normal form model offer springboard concepts for understanding and control in more sophisticated systems such as neural dynamics, soft robotics, or fixed action patterns observed in animals.