Noise effect on the signal transmission in an underdamped fractional coupled system
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ORIGINAL PAPER
Noise effect on the signal transmission in an underdamped fractional coupled system Suchuan Zhong · Lu Zhang
Received: 9 April 2020 / Accepted: 19 October 2020 © Springer Nature B.V. 2020
Abstract The signal transmission phenomenon in an underdamped fractional system composed of two harmonically coupled particles, but only the first particle, which is driven by a periodic force, is studied. We obtain the analytical expressions for the steadystate response of the two coupled particles by applying the stochastic averaging method and define the signal transmission factor to characterize signal transmission efficiency. We analyze the impact of noise on signal transmission efficiency and provide the discriminant criterion for the emergence of the signal transmission enhancement phenomenon. We also analyze the resonance behavior of the signal transmission factor and provide the discriminant criterion for the emergence of different types of resonance behavior based on system parameters. We draw the phase diagrams for varying resonance behavior versus different parameters and study the influences of the parameters on resonance behavior. It is found that the coupling strength and fractional-order exert important influences on the signal transmission efficiency and resonance behavior, and the fractional coupled system exhibits complicated S. Zhong Center of Aerospace Information Processing and Application, School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, People’s Republic of China e-mail: [email protected] L. Zhang (B) School of Mathematics, Sichuan University, Chengdu 610065, People’s Republic of China e-mail: [email protected]
dynamic behaviors than the integer coupled system. Lastly, numerical simulations for the signal transmission factor η, and the output signal-to-noise ratio (SNR) transmission gain SNRη are performed. We can control signal transmission efficiency and resonance behavior within a certain range by understanding the effects of system parameters on the underdamped fractional coupled system, and it has potential applications in modern science. Keywords Underdamped fractional coupled system · Steady-state response · Signal transmission factor · Signal transmission efficiency · Resonance behavior
1 Introduction Noise is ubiquitous in nature, and the constructive role of noise, particularly noise-induced complex dynamic behavior, such as noise-induced phase transition [1,2], stochastic resonance (SR) [3–5], coherent resonance [6–8], vibrational resonance [9–11], and Brownian motor [12–14], has been intensively investigated in recent decades. In particular, SR has drawn considerable research interests. Traditional SR means that appropriate noise can improve system response in a bistable system at the frequency of the input signal. That is, noise can induce or enhance temporal order in the dynamics of certain nonlinear systems. Coupled systems, i.e., systems with finite (or infinite) locally (or globally) coupled elements, represent
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S. Zhong, L. Zhang
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