Dynamics of electromechanical oscillators with static and time-varying potentials: bifurcation, dynamical integrity and activation maps

Abstract

Nonlinear oscillators with bistable potential energy landscapes exhibit complex dynamical responses that are highly sensitive to system parameters and initial conditions. In this work, we introduce a comparative framework for electromechanical oscillators with static potential energy (SPE) and time-varying potential energy (TVPE). The comparison is based on bifurcation analysis and global dynamical integrity assessment, which is proposed here as a guiding paradigm for nonlinear oscillator design. Results show that TVPE oscillators enable a more robust activation of large-amplitude regimes through temporal modulation of the potential barrier, whereas SPE systems exhibit strong sensitivity to parameters such as electrical load resistance and gap distance that however can be used to manipulate effectively the dynamic response. Furthermore, the proposed activation map framework extends robustness assessment to time-varying potential systems, providing a complementary tool to classical basin-based dynamical integrity analysis.