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Bifurcation and transition analysis of multiple attractors wind-induced vibration energy harvesting system with time-delayed feedback under Lévy noise

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Abstract

To improve the energy harvesting performance of the multiple attractors wind-induced vibration energy harvester under Lévy noise, the time-delayed feedback control is introduced in this paper. The influence mechanism of time-delayed feedback on the bifurcation of the deterministic system is discussed through parameter bifurcation diagrams and phase diagrams. For the system with noise disturbance, both Lévy noise and time-delayed feedback can significantly control stochastic P-bifurcation. Furthermore, we calculated the mean square voltage (MSV) of the system with several different time-delayed feedback parameters to find an effective way to enhance the energy harvesting performance. When other parameters remain unchanged, the optimal time-delayed feedback parameters can be selected to maximize the MSV. In addition, the first escape probability (FEP) is calculated to reveal the transition mechanism of the system from the low-amplitude region to the high-amplitude region. The results show that the time-delayed feedback can control the system to escape to a larger amplitude region. This research hopes to provide a theoretical reference for the design of high-performance energy harvesters.

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Data Availability

The data that support the finding of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors thank the reviewer for their careful reading and suggestions. This research was supported by the National Natural Science Foundation of China (Grant Nos.: 12072261, 11872305, 11972291).

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  1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, People’s Republic of China

    Wenting Zhang, Wei Xu, Yaning Tang & Yisha Lu

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  1. Wenting Zhang
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Correspondence to Wenting Zhang.

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Zhang, W., Xu, W., Tang, Y. et al. Bifurcation and transition analysis of multiple attractors wind-induced vibration energy harvesting system with time-delayed feedback under Lévy noise. Nonlinear Dyn 111, 10791–10808 (2023). https://doi.org/10.1007/s11071-023-08417-7

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