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

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. © 2017 Elsevier B.V. All rights reserved. * Corresponding author. ** Correspondence to: Web Sciences center, University of Electronic Science and Technology of China, Chengdu 610054, PR China. E-mail addresses: [email protected] (Y. Tian), [email protected] (L.-F. Zhong). http://dx.doi.org/10.1016/j.physa.2017.08.051 0378-4371/© 2017 Elsevier B.V. All rights reserved. 846 Y. Tian et al. / Physica A 490 (2018) 845–856