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

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.