TY - JOUR
T1 - Stochastic resonance in an underdamped triple-well potential system
AU - Xu, Pengfei
AU - Jin, Yanfei
AU - Zhang, Yanxia
N1 - Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - In this paper, stochastic resonance (SR) in an underdamped triple-well potential system driven by Gaussian white noise and a parametric harmonic excitation is investigated. The analytical expressions of the output signal-to-noise ratio (SNR), together with the mean first-passage times (MFPTs), are derived for the triple-well potential system involving damping in adiabatic limit. The effects of noise intensity, damping coefficient and triple-well potential on MFPTs and SNR are analyzed. The results suggest the existence of two critical damping values, giving rise to the onset and the disappearance of SR, respectively. Since the system is unstable in weak damping regime, emergence of SR is prohibited. Under the weak noise level, SNR exhibits a prominent resonance-like behavior at the optimal value of damping coefficient. Moreover, the two nonlinear stiffness coefficients of restoring force play an opposite role in the enhancement of SR. Thus, the SR effect significantly depends on the change of the two-side potential wells. Particularly, the appropriate choice of triple-well potential function and damping coefficient can improve the response of the system to an external periodic excitation according to the damping-induced resonance effect. Finally, the numerical results confirm the effectiveness of the theoretical analyses.
AB - In this paper, stochastic resonance (SR) in an underdamped triple-well potential system driven by Gaussian white noise and a parametric harmonic excitation is investigated. The analytical expressions of the output signal-to-noise ratio (SNR), together with the mean first-passage times (MFPTs), are derived for the triple-well potential system involving damping in adiabatic limit. The effects of noise intensity, damping coefficient and triple-well potential on MFPTs and SNR are analyzed. The results suggest the existence of two critical damping values, giving rise to the onset and the disappearance of SR, respectively. Since the system is unstable in weak damping regime, emergence of SR is prohibited. Under the weak noise level, SNR exhibits a prominent resonance-like behavior at the optimal value of damping coefficient. Moreover, the two nonlinear stiffness coefficients of restoring force play an opposite role in the enhancement of SR. Thus, the SR effect significantly depends on the change of the two-side potential wells. Particularly, the appropriate choice of triple-well potential function and damping coefficient can improve the response of the system to an external periodic excitation according to the damping-induced resonance effect. Finally, the numerical results confirm the effectiveness of the theoretical analyses.
KW - Mean first-passage time
KW - Signal-to-noise ratio
KW - Stochastic resonance
KW - Underdamped triple-well potential system
UR - http://www.scopus.com/inward/record.url?scp=85055912121&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2018.10.060
DO - 10.1016/j.amc.2018.10.060
M3 - Article
AN - SCOPUS:85055912121
SN - 0096-3003
VL - 346
SP - 352
EP - 362
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -