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Chin. Phys. B, 2021, Vol. 30(6): 060502    DOI: 10.1088/1674-1056/abd9b0
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Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency

Lei Jiang(姜磊)1, Li Lai(赖莉)1, Tao Yu(蔚涛)1,†, Maokang Luo(罗懋康)1,2
1 College of Mathematics, Sichuan University, Chengdu 610064, China;
2 College of Aeronautics and Astronautics, Sichuan University, Chengdu 610064, China
Abstract  The collective behaviors of two coupled harmonic oscillators with dichotomous fluctuating frequency are investigated, including stability, synchronization, and stochastic resonance (SR). First, the synchronization condition of the system is obtained. When this condition is satisfied, the mean-field behavior is consistent with any single particle behavior in the system. On this basis, the stability condition and the exact steady-state solution of the system are derived. Comparative analysis shows that, the stability condition is stronger than the synchronization condition, that is to say, when the stability condition is satisfied, the system is both synchronous and stable. Simulation analysis indicates that increasing the coupling strength will reduce the synchronization time. In weak coupling region, there is an optimal coupling strength that maximizes the output amplitude gain (OAG), thus the coupling-induced SR behavior occurs. In strong coupling region, the two particles are bounded as a whole, so that the coupling effect gradually disappears.
Keywords:  coupled harmonic oscillators      dichotomous fluctuating frequency      synchronization      stability      stochastic resonance  
Received:  10 November 2020      Revised:  03 January 2021      Accepted manuscript online:  08 January 2021
PACS:  05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)  
  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Xt (Synchronization; coupled oscillators)  
  05.90.+m (Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems)  
Fund: Project supported by the National Natural Science Foundation of China for the Youth (Grant Nos. 11501385 and 11801385).
Corresponding Authors:  Tao Yu     E-mail:

Cite this article: 

Lei Jiang(姜磊), Li Lai(赖莉), Tao Yu(蔚涛), Maokang Luo(罗懋康) Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency 2021 Chin. Phys. B 30 060502

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