Statistical complexity and stochastic resonance of an underdamped bistable periodic potential system excited by Lévy noise

Abstract

This paper focuses on the underdamped bistable potential system's stochastic resonance (SR) phenomenon under Lévy noise excitation. The statistical complexity of the system is analyzed under the changes of damping factor, amplitude and frequency of the periodic signal, stability index and skew parameter of Lévy noise, and the effects of the changes of above parameters on SR are investigated. The results show that the increase of the damping factor hinders the appearance of SR phenomenon; the larger amplitude and lower frequency of the periodic signal are beneficial to the appearance of SR; the larger stability index of the noise parameter, the more likely SR occurs, and the change of the skew parameter has little effect on the SR. Because the Bandt-Pompe (B-P) algorithm is used in the information-theoretic measure to model the statistical complexity of this system, the robustness of the method is analyzed by changing the embedding dimension and the length of residual time interval sequence in the B-P algorithm. Finally, the mean first passage time of the particle is calculated as a function of the noise intensity and the noise-enhanced stability effect is found.