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Stochastic bifurcations in a nonlinear tri-stable energy harvester under colored noise. (English) Zbl 1459.34134

Summary: In this paper, the stochastic bifurcations and the performance analysis of a strongly nonlinear tri-stable energy harvesting system with colored noise are investigated. Using the stochastic averaging method, the averaged Fokker-Plank-Kolmogorov equation and the stationary probability density (SPD) of the amplitude are obtained, respectively. Meanwhile, the Monte Carlo simulations are performed to verify the effectiveness of the theoretical results. D-bifurcation is studied through the largest Lyapunov exponent calculations, which implies the system undergoes D-bifurcation twice with increasing the nonlinear stiffness coefficients. The effects of the nonlinear stiffness coefficients, noise intensity and correlation time on P-bifurcation are discussed by the qualitative changes of the SPD. Moreover, the relationship between D- and P-bifurcation is explored. If the strength of stochastic jump has obvious gap with respect to the two statuses before and after the occurrence of P-bifurcation, the D-bifurcation will happen, too. Finally, the performance and the capability of harvesting energy from ambient random excitation are analyzed.

MSC:

34F10 Bifurcation of solutions to ordinary differential equations involving randomness
34C29 Averaging method for ordinary differential equations
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