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Tristable piezoelectric energy harvesters (TPEHs) have been widely studied in recent years. Previous works have illustrated the persistent coexistence of high-energy and low-energy responses. Jumps among the responses can be induced by unavoidable initial-condition disturbances of TPEHs in practice, which concerns the final output of the harvested energy. For a more accurate evaluation of the TPEH performance, the disturbances of initial conditions should be taken into account. This study focuses on global dynamics of a typical TPEH with two fixed external magnets. Via static bifurcation analysis of the TPEH oscillatory system, the separation and gap distances are identified as key parameters to configure triple potential wells. The primary resonance analysis of the intra-well and inter-well responses is carried out to determine the optimum separation distance for efficient energy harvesting. Then, sequences of attractors and their basins of attraction (BAs) with the rise in the ambient excitation level and frequency is illustrated, showing that initial conditions of the TPEH system perturbed within the central well are beneficial for energy harvesting. For a low-level base excitation, BAs outside of the triple wells are severely fractal where the perturbation of the initial state of the TPEH can easily induce a jump that implies the unreliability of the TPEH performance. At a much higher ambient excitation level, the high-energy inter-well response can be globally attractive and reliable, which is preferable for practical applications of energy harvesters. • The key structural parameter of the TPEH is selected via static bifurcation analysis for configuring the potential wells. • Influence of the ambient excitation on the intra-well and inter-well resonant responses of the TPEH system is discussed. • BAs under different excitation levels and frequencies are depicted for reliably evaluating the performance of the TPEH. • Complex dynamical behaviors such as high-order responses, rare and hidden attractors, and fractal BAs are detected. [ABSTRACT FROM AUTHOR]

Abstract: Three types of delayed feedbacks, namely, the delayed position feedback (DPF), delayed velocity feedback (DVF) and delayed state feedback (DSF), are proposed to control the erosion of safe basins in a parametrically excited system. The time delay and the gain in the feedbacks are chosen as control parameters. The safe basin erosion is measured by the size and nature of the safe basin. The nature of the safe basin, fractal or smooth, is investigated by evaluating the fractal dimension. The critical values of the control parameters are obtained for any points in the safe basin not to be eroded. It is concluded that delayed feedbacks can be applied to control the extent of the erosion. Moreover, the comparison among the effects of the three types of delayed feedbacks reveals that DPF is the best strategy to reduce the fractal erosion of safe basins at small values of the delay and the gain, while DSF becomes the best when the delay or the gain is large. [Copyright &y& Elsevier]