Thermal Control of Hysteresis and Deterministic Chaos in a Memristive MEMS Resonator

Abstract

We investigate the nonlinear dynamics of a thermo-electro-mechanically coupled memristive resonator comprising a doubly clamped Euler--Bernoulli microbeam, an RLC circuit, and a TiO$_2$ memristor with temperature-dependent ionic mobility governed by Mott and Efros--Shklovskii hopping conduction. The dynamics are analyzed using two-dimensional parameter-space maps, bifurcation diagrams, Lyapunov exponents, reconstructed attractors, Poincar\'e sections, Grassberger--Procaccia correlation-dimension analysis, empirical mode decomposition, the Hilbert--Huang spectrum, and electro-memristive hysteresis. Parameter-space maps reveal predominantly quasi-periodic and deterministic chaotic regimes without stable phase-locked periodic states. Bifurcation analyses show that the beam length and excitation frequency govern the dynamics through the frequency ratio $r_\omega=\omega_0/\omega_b$, whereas the excitation current mainly controls the oscillation amplitude and chaotic intensity. Under fixed operating conditions, the asymptotic regime depends on the initial conditions, and complementary diagnostics identify the thermo-memristive subsystem as the primary source of the nonlinear complexity, subsequently transmitted to the microbeam through electromechanical coupling. Temperature continuously reorganizes the electro-memristive hysteresis through the chain $T \to \sigma(T) \to M(w,T) \to i_m(t) \to w(t)$. The hysteresis area evolves non-monotonically with temperature, revealing a configuration-dependent optimal thermo-memristive operating point. These findings highlight temperature, beam length, and electrical excitation as complementary control parameters for tailoring thermo-memristive memory, deterministic chaos, and nonlinear dynamics in thermo-active MEMS, with potential applications in neuromorphic sensing and chaos-based secure communication.