Nonlinear effect of time delay on the generalized stochastic resonance in a fractional oscillator with multiplicative polynomial noise

We investigate generalized stochastic resonance (GSR) in a fractional harmonic oscillator with time delay and fluctuation damping. Considering that nonlinear noise widely exists in actual systems compared with linear noise, the fluctuation of damping is modeled as polynomial trichotomous noise. The...

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Bibliographic Details
Published in:Nonlinear dynamics 2017-07, Vol.89 (2), p.1327-1340
Main Authors: Zhong, Suchuan, Zhang, Lu, Wang, Huiqi, Ma, Hong, Luo, Maokang
Format: Article
Language:English
Subjects:
Amplitudes
Approximation
Automotive Engineering
Classical Mechanics
Computer simulation
Control
Damping
Delay
Dynamical Systems
Engineering
Functions (mathematics)
Harmonic oscillators
Mechanical Engineering
Noise
Nonlinear phenomena
Original Paper
Parameters
Phase diagrams
Polynomials
Probability theory
Stochastic resonance
Time lag
Variations
Vibration
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Summary:We investigate generalized stochastic resonance (GSR) in a fractional harmonic oscillator with time delay and fluctuation damping. Considering that nonlinear noise widely exists in actual systems compared with linear noise, the fluctuation of damping is modeled as polynomial trichotomous noise. The analytical expression of the output amplitude gain is derived by applying small delay approximation and stochastic averaging. Simulation results show that the output amplitude gain curves, as functions of time delay versus noise parameters, behave non-monotonically and exhibit typical GSR. Furthermore, nonlinear phenomena of stochastic multi-resonance with two, three, and four peaks are observed. Finally, we provide the phase diagrams for GSR versus time delay with different system parameters. Furthermore, the mechanism underlying the stochastic multi-resonance with two, three, and four peaks, as well as their connections, is elucidated. This study could serve as a theoretical basis for the practical use and control of GSR in future works.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-017-3518-x