Noise-induced Dynamics in a Delayed Triple-well Potential System Driven by Correlated Noises

In this paper, the effects of time delay and correlated noises on noise-induced dynamics in a delayed triple-well potential system are studied. Using the linear response theory, we derive the expression of the transient response to show the effectiveness of the system response to a periodic forcing. The effectiveness of the system response to an external forcing can be improved in a triple-well system by choosing the proper time delay and noise cross-correlation. Moreover, the power spectrum and the quality factor are calculated to quantify coherence resonance (CR). It is found that the power spectrum and the quality factor show the peak structure as the optimal noise intensities are chosen. That is, the CR appears in this system. The noise cross-correlation can break the symmetry of the triple-well potential and induce the transition of the interwell resonance among different wells. The presence of time delay in the triple-well potential enhances the role of multiplicative noise in the regularity dynamics.