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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]

In the military arms race, the focus of the defender is on selecting the optimal development plan of armaments, i.e., advantageous defense resources allocation. As an indispensable feature of armaments, the cooperative interactions between different armaments influence their effectiveness directly, but they have not been elaborated yet in the existing study. In this regard, a mathematical formulation, named operation loop, is proposed to investigate the cooperative interactions between armaments, sequentially facilitating the description of the development plans’ performance. Additionally, the defender's development plans of armaments depend much on the attacker's weapons, bringing the characteristics of multiobjective into this problem. Furthermore, the uncertainty about the development plans of the attacker has been taken into consideration as well. Therefore, the paper concentrates on formulating the resources allocation problem with incomplete information as a network design problem. By optimizing the network design using covariance matrix adaptation evolution strategy, an effective armaments development plan can be obtained. The feasibility is demonstrated by a case study.

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]

A delayed position feedback control is applied on DC voltage source for suppressing chaos of a typical MEMS resonator actuated by electrostatic forces. A theoretical necessary condition for chaotic oscillation of the controlled system is presented. Numerical results and the analytical prediction reveal the evolution of dynamical behavior of the system with AC voltage amplitude and the control effect of delayed feedback on reducing chaos of the system. It shows that the delayed feedback control is effective on suppressing chaos of the micro mechanical resonator.