Characterization of quasi-periodic and chaotic dynamics in a memristive MEMS: parameter-induced transitions and thermo-sensitive modulation

Abstract

This work presents the mathematical modeling and numerical characterization of a Micro-Electro-Mechanical System (MEMS) integrating an HP memristor coupled to electrical and mechanical resonators. Based on the linear-drift HP memristor model, the nonlinear electromechanical dynamics are investigated through Lyapunov exponents, bifurcation diagrams, Poincaré sections, recurrence plots, phase portraits, and Fourier spectra. The numerical results demonstrate that the intrinsic memristor parameters, namely the low-resistance state \(R_{on}\), the high-resistance state \(R_{off}\), the oxide thickness D, and the ionic mobility \(\mu _{v}\), directly control the amplitude, frequency content, and dynamical regime of the electromechanical oscillations, inducing transitions between quasi-periodic and chaotic behaviors. Temperature-dependent variations of these memristive parameters are shown to modulate both the oscillation amplitudes and the distribution of quasi-periodic and chaotic regimes, highlighting the thermo-sensitive character of the proposed architecture. A qualitative comparison with Josephson-junction-based MEMS is provided, emphasizing that the HP memristor exhibits similar nonlinear dynamical features while remaining fully operational at room temperature. These results suggest that memristive thermo-sensitive MEMS constitute a promising platform for adaptive nonlinear oscillators, thermo-sensitive sensing devices, and chaos-assisted electromechanical applications.