Please wait a minute...
Chin. Phys. B, 2021, Vol. 30(6): 060502    DOI: 10.1088/1674-1056/abd9b0
GENERAL Prev   Next  

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:  scuyutao@163.com

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

[1] Benzi R, Sutera A and Vulpiani A 1981 J. Phys. A 14 L453
[2] Benzi R, Parisi G, Sutera A and Vulpiani A 1982 Tellus 34 10
[3] Nicolis C 1982 Tellus 34 1
[4] Gammaitoni L, Ha${\rm{\ddot n}}$ggi P, Jung P and Marchesoni F 1998 Rev. Mod. Phys. 70 223
[5] Ha${\rm{\ddot n}}$ggi P, Jung P, Zerbe C and Moss F 1993 J. Stat. Phys. 70 25
[6] McNamara B and Wiesenfeld K 1989 Phys. Rev. A 39 4854
[7] Fox R F 1989 Phys. Rev. A 39 4148
[8] Gang H, Ditzinger T, Ning C Z and Haken H 1993 Phys. Rev. Lett. 71 807
[9] Tessone C J, Mirasso C R, Toral R and Gunton J D 2006 Phys. Rev. Lett. 97 194101
[10] Atsumi Y, Hata H and Nakao H 2013 Phys. Rev. E 88 052806
[11] Tang Y, Zou W, Lu J and Kurths J 2012 Phys. Rev. E 85 046207
[12] Pikovsky A, Zaikin A and de la Casa M A 2002 Phys. Rev. Lett. 88 050601
[13] Cubero D 2008 Phys. Rev. E 77 021112
[14] Li J H 2002 Phys. Rev. E 66 031104
[15] Gitterman M 2005 Physica A 352 309
[16] Li J H and Han Y X 2006 Phys. Rev. E 74 051115
[17] Li J H and Han Y X 2007 Commun. Theor. Phys. 47 672
[18] Jiang S, Guo F, Zhou Y and Gu T 2007 Physica A 375 483
[19] Li J H 2011 Chaos 21 043115
[20] He G T, Tian Y and Wang Y 2013 J. Stat. Mech. 9 26
[21] He G T, Luo R Z and Luo M K 2013 Phys. Scr. 88 065009
[22] Yu T, Zhang L and Luo M K 2013 Phys. Scr. 88 045008
[23] He G T, Tian Y and Luo M K 2014 J. Stat. Mech. 2014 P05018
[24] Zhong S C, Ma H, Peng H and Zhang L 2015 Nonlinear Dyn. 82 535
[25] Chandrasekhar S 1943 Rev. Mod. Phys. 15 1
[26] Sauga A, Mankin R and Ainsaar A 2012 AIP Conf. Proc. 1487 224
[27] Lang R L, Yang L, Qin H L and Di G H 2012 Nonlinear Dyn. 69 1423
[28] Mankin R, Laas K, Laas T and Reiter E 2008 Phys. Rev. E 78 031120
[29] Soika R, Mankin R and Ainsaar A 2010 Phys. Rev. E 81 011141
[30] Laas K, Mankin R and Rekker A 2009 Phys. Rev. E 79 051128
[31] Yang B, Zhang X, Zhang L and Luo M K 2016 Phys. Rev. E 94 022119
[32] Boccaletti S, Latora V, Moreno Y, Chavez M and Hwang D U 2006 Phys. Rep. 424 175
[33] Nicolis C and Nicolis G 2017 Phys. Rev. E 96 042214
[34] Droste F and Lindner B 2014 Biol. Cybern. 108 825
[35] Reimann P and Elston T C 1996 Phys. Rev. Lett. 77 5328
[36] Si M, Conrad N, Shin S, Gu J, Zhang J, Alam M and Ye P 2015 IEEE Trans. Electron Dev. 62 3508
[37] Van Den Broeck C 1983 J. Stat. Phys. 31 467
[38] Vishwamittar, Batra P and Chopra R 2021 Physica A 561 125148
[39] Wojciech S and Dariusz W 2020 Commun. Nonlinear Sci. Numer. Simulat. 83 105099
[40] Emelyanov Y P, Emelyanov V V and Ryskin N M 2014 Commun. Nonlinear Sci. Numer. Simulat. 19 3778
[41] Shapiro V E and Loginov V M 1978 Physica A 91 563
[42] Dorf R C and Bishop R H 2010 Modern Control Systems, 12th edn. (Pearson: Prentice Hall)
[43] Fulinski A 1993 Phys. Lett. A 180 94
[44] Robertson B and Astumian R D 1991 J. Chem. Phys. 94 7414
[45] Kubo R 1963 J. Math. Phys 4 174
[46] Berdichevsky V and Gitterman M 1996 Europhys. Lett 36 161
[47] Jiang S Q, Hou M J, Jia C H, He J R and Gu T X 2009 Chin. Phys. B 18 2667
[48] Astumian R D and Bier M 1994 Phys. Rev. Lett. 72 1766
[49] Li J H and Huang Z Q 1998 Phys. Rev. E 57 3917
[50] Bier M 1997 Contemp. Phys. 38 371
[51] Li J H, Chen Q H and Zhou X F 2010 Phys. Rev. E 81 041104
[52] Wang Q, Perc M, Duan Z and Chen G 2009 Chaos 19 023112
[53] Hendricks A G, Epureanu B I and Meyhofer E 2009 Phys. Rev. E 79 031929
[54] Stukalin E B, Phillips III H and Kolomeisky A B 2005 Phys. Rev. Lett. 94 238101
[55] Kim C, Lee E K and Talkner P 2006 Phys. Rev. E 73 026101
[1] Explosive synchronization in a mobile network in the presence of a positive feedback mechanism
Dong-Jie Qian(钱冬杰). Chin. Phys. B, 2022, 31(1): 010503.
[2] Identification of unstable individuals in dynamic networks
Dongli Duan(段东立), Tao Chai(柴涛), Xixi Wu(武茜茜), Chengxing Wu(吴成星), Shubin Si(司书宾), and Genqing Bian(边根庆). Chin. Phys. B, 2021, 30(9): 090501.
[3] Dynamic modeling and aperiodically intermittent strategy for adaptive finite-time synchronization control of the multi-weighted complex transportation networks with multiple delays
Ning Li(李宁), Haiyi Sun(孙海义), Xin Jing(靖新), and Zhongtang Chen(陈仲堂). Chin. Phys. B, 2021, 30(9): 090507.
[4] Stability of liquid crystal systems doped with γ-Fe2O3 nanoparticles
Xu Zhang(张旭), Ningning Liu(刘宁宁), Zongyuan Tang(唐宗元), Yingning Miao(缪应宁), Xiangshen Meng(孟祥申), Zhenghong He(何正红), Jian Li(李建), Minglei Cai(蔡明雷), Tongzhou Zhao(赵桐州), Changyong Yang(杨长勇), Hongyu Xing(邢红玉), and Wenjiang Ye(叶文江). Chin. Phys. B, 2021, 30(9): 096101.
[5] A sign-function receiving scheme for sine signals enhanced by stochastic resonance
Zhao-Rui Li(李召瑞), Bo-Hang Chen(陈博航), Hui-Xian Sun(孙慧贤), Guang-Kai Liu(刘广凯), and Shi-Lei Zhu(朱世磊). Chin. Phys. B, 2021, 30(8): 080502.
[6] Low-threshold bistable reflection assisted by oscillating wave interaction with Kerr nonlinear medium
Yingcong Zhang(张颖聪), Wenjuan Cai(蔡文娟), Xianping Wang(王贤平), Wen Yuan(袁文), Cheng Yin(殷澄), Jun Li(李俊), Haimei Luo(罗海梅), and Minghuang Sang(桑明煌). Chin. Phys. B, 2021, 30(8): 084203.
[7] Modeling of cascaded high isolation bidirectional amplification in long-distance fiber-optic time and frequency synchronization system
Kuan-Lin Mu(穆宽林), Xing Chen(陈星), Zheng-Kang Wang(王正康), Yao-Jun Qiao(乔耀军), and Song Yu(喻松). Chin. Phys. B, 2021, 30(7): 074208.
[8] Low-dimensional phases engineering for improving the emission efficiency and stability of quasi-2D perovskite films
Yue Wang(王月), Zhuang-Zhuang Ma(马壮壮), Ying Li(李营), Fei Zhang(张飞), Xu Chen(陈旭), and Zhi-Feng Shi (史志锋). Chin. Phys. B, 2021, 30(6): 067802.
[9] Time-varying coupling-induced logical stochastic resonance in a periodically driven coupled bistable system
Yuangen Yao(姚元根). Chin. Phys. B, 2021, 30(6): 060503.
[10] $\mathcal{H}_{\infty }$ state estimation for Markov jump neural networks with transition probabilities subject to the persistent dwell-time switching rule
Hao Shen(沈浩), Jia-Cheng Wu(吴佳成), Jian-Wei Xia(夏建伟), and Zhen Wang(王震). Chin. Phys. B, 2021, 30(6): 060203.
[11] Improved nonlinear parabolized stability equations approach for hypersonic boundary layers
Shaoxian Ma(马绍贤), Yi Duan(段毅), Zhangfeng Huang(黄章峰), and Shiyong Yao(姚世勇). Chin. Phys. B, 2021, 30(5): 054701.
[12] Improvement of the short-term stability of atomic fountain clock with state preparation by two-laser optical pumping
Lei Han(韩蕾), Fang Fang(房芳), Wei-Liang Chen(陈伟亮), Kun Liu(刘昆), Shao-Yang Dai(戴少阳), Ya-Ni Zuo(左娅妮), and Tian-Chu Li(李天初). Chin. Phys. B, 2021, 30(5): 050602.
[13] A simplified approximate analytical model for Rayleigh-Taylor instability in elastic-plastic solid and viscous fluid with thicknesses
Xi Wang(王曦), Xiao-Mian Hu(胡晓棉), Sheng-Tao Wang(王升涛), and Hao Pan(潘昊). Chin. Phys. B, 2021, 30(4): 044702.
[14] Performance and stability-enhanced inorganic perovskite light-emitting devices by employing triton X-100
Ao Chen(陈翱), Peng Wang(王鹏), Tao Lin(林涛), Ran Liu(刘然), Bo Liu(刘波), Quan-Jun Li(李全军), and Bing-Bing Liu(刘冰冰). Chin. Phys. B, 2021, 30(4): 048506.
[15] Stability and optoelectronic property of low-dimensional organic tin bromide perovskites
J H Lei(雷军辉), Q Tang(汤琼), J He(何军), and M Q Cai(蔡孟秋). Chin. Phys. B, 2021, 30(3): 038102.
No Suggested Reading articles found!