Coherence and stochastic resonance in a second-order asymmetric tri-stable system with memory effects

In this paper, the phenomena of coherence resonance (CR) and stochastic resonance (SR) are studied in an asymmetric tri-stable potential with memory effects, which is driven by internal noise and a periodic forcing. Analytical expressions for characteristic correlation time and spectral amplification are derived to quantify the CR and the SR, respectively. The obtained results indicate the existence of a critical value of asymmetry for the onset of CR. For intermediate memory times, there exhibits an optimal memory intensity at which the CR attains maximum. Moreover, memory plays a significant role in an enhancement of CR and SR, which also depends prominently on the tri-stable potential structure. Interestingly, memory time suppresses CR but enhances SR. Specifically, the appropriate choice of asymmetry constant and nonlinear stiffness coefficient can improve the performance of system response to an external periodic signal based on the SR effect. Finally, the results from numerical simulations well verify the validity of the theoretical analyses.