Stochastic resonance and bifurcations in a harmonically driven tri-stable potential with colored noise

Stochastic resonance (SR) and stochastic bifurcations are investigated numerically in a nonlinear tri-stable system driven by colored noise and a harmonic excitation. The power spectral density, signal-to-noise ratio, stationary probability density (SPD), and largest Lyapunov exponent (LLE) are calculated to quantify SR, P-bifurcation, and D-bifurcation, respectively. The effects of system parameters, such as noise intensity and correlation time, well-depth ratio, and damping coefficient, on SR and stochastic bifurcations are explored. Numerical results show that both noise-induced suppression and SR can be observed in this system. The SPD changes from bimodal to trimodal and then to the unimodal structure by choosing well-depth ratio, correlation time, and noise intensity as bifurcation parameters, which shows the occurrence of stochastic P-bifurcation. The stochastic D-bifurcation is found through the calculation of LLE. Moreover, the relationship between SR and stochastic bifurcation is explored thoroughly. It indicates that the optimal SR occurs near D-bifurcation and can be realized with weak chaos by adjusting the proper parameters. Finally, the tri-stable energy harvester is chosen as an example to show the improvement of the system performance by exploiting SR and stochastic bifurcations.