Successive Torus-Doubling Route to Chaos in Quasi-Zero Stiffness Energy Harvester

In this work, we investigate the nonlinear dynamics of a Quasi-Zero Stiffness Energy Harvester (QZEH) under quasi-periodic forcing and report a successive localized torus-doubling route that leads to the formation of a Strange Nonchaotic Attractor (SNA), a phenomenon not previously documented in QZEH systems. The presence of the SNA is verified through multiple characterization techniques, including Lyapunov exponents, finite-time Lyapunov statistics, recurrence-based Shannon entropy, and singular continuous spectral analysis. A key methodological contribution of this study is the introduction of a finite-time energy-variance diagnostic that quantifies the consistency of harvested energy across different dynamical regimes. By analyzing the variance of the energy generated over sliding time windows, we show that tori yield low but highly stable energy output, chaotic attractors produce high yet strongly irregular energy, and SNAs provide an intermediate energy level with substantially lower variability than chaos. This reveals SNAs as a favorable compromise between energy yield and robustness.