Characterization of Chaotic and Homogeneous coexisting dynamics of a Memristive Thermo-Controlled MEMS

Abstract

This work presents the mathematical modeling and numerical investigation of a thermo-controlled Micro-Electro-Mechanical System (MEMS) obtained by coupling an HP memristor with mechanical and electrical resonators. Using the linear drift HP memristor model, the nonlinear electromechanical dynamics are analyzed through Lyapunov exponents, bifurcation diagrams, phase portraits, recurrence plots, Poincaré sections, and Fourier spectra. The results reveal parameter-dependent transitions between quasi-periodic and chaotic oscillations, as well as signatures of coexisting dynamical regimes. A systematic investigation of the intrinsic memristor parameters, namely the ON-state resistance Ron, the OFF-state resistance Roff, the oxide thickness D, and the ionic mobility μ_v, demonstrates that memristive effects strongly influence oscillation amplitudes, resonance frequencies, and nonlinear transitions within the coupled thermo-electro-mechanical system. The state-dependent memristance dynamically modulates the electromechanical coupling and redistributes energy between the electrical and mechanical resonators, thereby generating complex oscillatory responses. In addition, the influence of temperature-sensitive memristive parameters is qualitatively examined through variations of the ionic mobility and resistive states. The results indicate that thermal variations can modify both oscillation amplitudes and dynamical regimes, potentially inducing transitions between quasi-periodic and chaotic behaviors. A comparative discussion with Josephson-junction-based MEMS architectures highlights the operational flexibility and room-temperature compatibility of the HP memristor model for thermo-electro-mechanical applications. These findings suggest promising prospects for adaptive nonlinear oscillators, thermo-sensitive sensors, and chaos-driven electromechanical systems.