Nonlinear response identification of a parametrically excited bistable magnetic rolling pendulum harvester by 0–1 test and recurrence plots

Owing to the low damping characteristics, magnetic rolling pendulum gains extensive adoption in vibration energy harvesting. Bistable magnetic rolling pendulum harvester (BMRPH) exhibits chaotic and (quasi-)periodic vibrational responses, and effectively identifying the complex dynamic behaviors is essential for advancing practical applications. Therefore, this paper utilizes 0–1 test and recurrence plot (RP) to examine the nonlinear voltage response time series of a parametrically excited BMRPH. By analyzing the nonlinear dynamics of the BMRPH, multiple vibrational patterns are emphasized. Results indicate that 0–1 test could easily distinguish between chaotic and periodic responses through the trajectory plot of (p, q), total mean square displacement, and asymptotic growth rate. Unlike 0–1 test, which provides a binary classification (0 for periodic and 1 for chaotic systems), RP offers a more nuanced approach by not only distinguishing between chaotic and periodic dynamics but also revealing the relative complexity within periodic regimes. In general, the identification results align well with complementary diagnostic methods, including phase portraits, Poincaré maps, frequency spectra, and multiscale entropy, thereby offering valuable insights for optimizing the dynamic performance and enhancing energy harvesting efficiency.