The resonant behavior in the oscillator with double fractional-order damping under the action of nonlinear multiplicative noise

• Published in: Physica A Vol. 490; pp. 845 - 856
• Main Authors: Tian, Yan, Zhong, Lin-Feng, He, Gui-Tian, Yu, Tao, Luo, Mao-Kang, Stanley, H. Eugene
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.01.2018
• Subjects: Nonlinear noise; Stochastic resonance; The fractional-order external damping; The fractional-order intrinsic damping; The fractional-order intrinsic damping; Nonlinear noise; The fractional-order external damping; Stochastic resonance
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2017.08.051

We study stochastic resonance (SR) in an oscillator with nonlinear noise, fractional-order external damping, and fractional-order intrinsic damping. Using a moment equation, we derive the exact analytical expression of the output amplitude and find that fluctuations in the output amplitude are non-monotonic. Using numerical simulations we verify the accuracy of this analytical result. We find (i) that nonlinear noise plays a key role in system behavior and that the resonance of the output amplitude is diverse when there is nonlinear noise, (ii) that the order of the fractional-order damping strongly impacts resonant intensity and that the impact on resonant intensity of fractional-order external damping is opposite that of fractional-order intrinsic damping, and (iii) that the evolution of the output amplitude versus the frequency of the external periodic force exhibits three behaviors: a resonance with one peak, a resonance with one peak and one valley, and a resonance with one valley. •SR is studied in the system with double fractional-order damping and nonlinear noise.•The resonance is diverse when there is nonlinear noise.•The order of the fractional-order damping strongly impacts resonant intensity.•The impact of external and intrinsic damping on resonant intensity is the opposite.