Nonlinear effects in a strongly coupled nanoelectromechanical system

Controlling nonlinear effects in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>μ</a:mi> </a:math> – and nanoelectromechanical systems is essential for unlocking their full potential in sensing, signal processing, and frequency control. In this study, we develop a voltage-dependent Hamiltonian framework for a nanoelectromechanical resonator with two strongly coupled vibrational modes, representative of a nanostring platform. The mode frequencies and couplings of the system are tuned electrostatically using a dc voltage, which also controls the strength of the interactions. Our theoretical model reproduces the experimentally observed avoided crossing in the absence of an ac drive and generates tunable frequency-comb spectra when a parametric drive is applied. By scanning the dc voltage, we generate a phase diagram that links comb formation and sharp regime boundaries to underlying bifurcations, multistability, and attractor switching. Phase-resolved diagnostics based on a Kuramoto order parameter, together with autocorrelation and Poincaré analyses, quantify coherence and critical slowing down near these transitions. We further explore the relationship between nonlinear coupling, parametric excitation, and stability transitions within a single device of experimental relevance and establish a dynamical framework for engineering nanoelectromechanical resonators that offer enhanced tunability, functionality, and a predictive link to experimental outcomes.