Effects of potential field delay and coupling delay on collective behavior of a fractional-order coupled system in a dichotomous fluctuating potential

doi:10.1088/1674-1056/adbd15

中国物理B ›› 2025, Vol. 34 ›› Issue (5): 50501-050501.doi: 10.1088/1674-1056/adbd15

Effects of potential field delay and coupling delay on collective behavior of a fractional-order coupled system in a dichotomous fluctuating potential

Yangfan Zhong(钟扬帆)¹, Xi Chen(陈熙)³, Maokang Luo(罗懋康)^1,2, and Tao Yu(蔚涛)^1,†

1 College of Mathematics, Sichuan University, Chengdu 610064, China;
2 College of Aeronautics and Astronautics, Sichuan University, Chengdu 610064, China;
3 The 10th Research Institute of China Electronics Technology Group Corporation, Chengdu 610066, China

收稿日期:2024-12-05 修回日期:2025-02-01 接受日期:2025-03-06 出版日期:2025-05-15 发布日期:2025-05-08
通讯作者: Tao Yu E-mail:scuyutao@163.com
基金资助:
Project supported by the Natural Science Foundation of Sichuan Province, China (Youth Science Foundation) (Grant No. 2022NSFSC1952).

Effects of potential field delay and coupling delay on collective behavior of a fractional-order coupled system in a dichotomous fluctuating potential

Yangfan Zhong(钟扬帆)¹, Xi Chen(陈熙)³, Maokang Luo(罗懋康)^1,2, and Tao Yu(蔚涛)^1,†

1 College of Mathematics, Sichuan University, Chengdu 610064, China;
2 College of Aeronautics and Astronautics, Sichuan University, Chengdu 610064, China;
3 The 10th Research Institute of China Electronics Technology Group Corporation, Chengdu 610066, China

Received:2024-12-05 Revised:2025-02-01 Accepted:2025-03-06 Online:2025-05-15 Published:2025-05-08
Contact: Tao Yu E-mail:scuyutao@163.com
Supported by:
Project supported by the Natural Science Foundation of Sichuan Province, China (Youth Science Foundation) (Grant No. 2022NSFSC1952).

摘要/Abstract

摘要： The collective dynamic of a fractional-order globally coupled system with time delays and fluctuating frequency is investigated. The power-law memory of the system is characterized using the Caputo fractional derivative operator. Additionally, time delays in the potential field force and coupling force transmission are both considered. Firstly, based on the delay decoupling formula, combined with statistical mean method and the fractional-order Shapiro-Loginov formula, the ``statistic synchronization'' among particles is obtained, revealing the statistical equivalence between the mean field behavior of the system and the behavior of individual particles. Due to the existence of the coupling delay, the impact of the coupling force on synchronization exhibits non-monotonic, which is different from the previous monotonic effects. Then, two kinds of theoretical expression of output amplitude gains $G$ and $\bar{G}$ are derived by time-delay decoupling formula and small delay approximation theorem, respectively. Compared to $\bar{G}$, $G$ is an exact theoretical solution, which means that $G$ is not only more accurate in the region of small delay, but also applies to the region of large delay. Finally, the study of the output amplitude gain $G$ and its resonance behavior are explored. Due to the presence of the potential field delay, a new resonance phenomenon termed ``periodic resonance'' is discovered, which arises from the periodic matching between the potential field delay and the driving frequency. This resonance phenomenon is analyzed qualitatively and quantitatively, uncovering undiscovered characteristics in previous studies.

关键词: potential field delay, coupling delay, fractional-order, collective behavior

Abstract: The collective dynamic of a fractional-order globally coupled system with time delays and fluctuating frequency is investigated. The power-law memory of the system is characterized using the Caputo fractional derivative operator. Additionally, time delays in the potential field force and coupling force transmission are both considered. Firstly, based on the delay decoupling formula, combined with statistical mean method and the fractional-order Shapiro-Loginov formula, the ``statistic synchronization'' among particles is obtained, revealing the statistical equivalence between the mean field behavior of the system and the behavior of individual particles. Due to the existence of the coupling delay, the impact of the coupling force on synchronization exhibits non-monotonic, which is different from the previous monotonic effects. Then, two kinds of theoretical expression of output amplitude gains $G$ and $\bar{G}$ are derived by time-delay decoupling formula and small delay approximation theorem, respectively. Compared to $\bar{G}$, $G$ is an exact theoretical solution, which means that $G$ is not only more accurate in the region of small delay, but also applies to the region of large delay. Finally, the study of the output amplitude gain $G$ and its resonance behavior are explored. Due to the presence of the potential field delay, a new resonance phenomenon termed ``periodic resonance'' is discovered, which arises from the periodic matching between the potential field delay and the driving frequency. This resonance phenomenon is analyzed qualitatively and quantitatively, uncovering undiscovered characteristics in previous studies.

Key words: potential field delay, coupling delay, fractional-order, collective behavior

中图分类号: (Stochastic analysis methods)

05.10.Gg

05.10.-a (Computational methods in statistical physics and nonlinear dynamics) 05.45.Xt (Synchronization; coupled oscillators) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)

Yangfan Zhong(钟扬帆), Xi Chen(陈熙), Maokang Luo(罗懋康), and Tao Yu(蔚涛). Effects of potential field delay and coupling delay on collective behavior of a fractional-order coupled system in a dichotomous fluctuating potential[J]. 中国物理B, 2025, 34(5): 50501-050501.

参考文献

[1] Gammaitoni L, Hänggi P, Jung P and Marchesoni F 1998 Rev. Mod. Phys. 70 223
[2] Benzi R, Sutera A and Vulpiani A 1981 J. Phys. A 14 L453
[3] Stroescu I, Hume D B and Oberthaler M K 2016 Phys. Rev. Lett. 117 243005
[4] Duan F, Pan Y, Chapeau-Blondeau F and Abbott D 2019 IEEE Trans. Signal Process 67 4611
[5] Mcnamara B and Wiesenfeld K 1989 Phys. Rev. A 39 4854
[6] Cubero D 2008 Phys. Rev. E 77 021112
[7] Jian L, Bing H, Fan Y, Chuan L Z and Xiao J D 2020 Commun. Nonlinear Sci. Numer. Simulat. 85 105245
[8] Gammaitoni L, Marchesoni F, Menichella-Saetta E and Santucci S 1994 Phys. Rev. E 49 4878
[9] Li JH 2002 Phys. Rev. E 66 031104
[10] Berdichevsky V and Gitterman M 1996 Europhys Lett. 36 161
[11] Gitterman M 2005 Physica A 352 309
[12] Yu T, Zhang L and Luo M K 2013 Phys. Scr. 88 045008
[13] Nicolis C and Nicolis G 2017 Phys. Rev. E 96 042214
[14] Tu Z, Zhao D Z, Qiu F and Yu T 2020 J. Stat. Phys. 179 247
[15] Jiang L, Lai L, Yu T and Luo M K 2021 Acta Phys. Sin. 70 130501 (in Chinese)
[16] Quintero-Quiroz C and Cosenza M G 2015 Chaos, Solitons and Fractals 71 41
[17] Massihi N, Parastesh F, Towhidkhah F, Huihai W, Shaobo H and Jafari S 2024 Europhys. Lett. 146 21005
[18] Zhong S C, Zhang L, Wang H Q, Ma H and Luo M K 2017 Nonlinear Dyn. 89 1327
[19] Raúl V S 2023 Commun. Nonlinear Sci. Numer. Simulat. 117 106934
[20] Lin L F, He M Y and Wang H Q 2022 Chaos, Solitons and Fractals 154 111641
[21] Liang X M, Tang M, Dhamala M and Liu Z H 2009 Phys. Rev. E 80 066202
[22] Zou W, Senthilkumar D V, Tang Y, Wu Y, Lu J Q and Kurths J 2013 Phys. Rev. E 88 032916
[23] Zhong Y F, Luo M K, Chen X and Yu T 2024 Commun. Nonlinear Sci. Numer. Simulat. 130 107799
[24] Zeitler M, Daffertshofer A and Gie-len CCAM 2009 Phys. Rev. E 79 065203
[25] Majer N and Schöll E 2009 Phys. Rev. E 79 011109
[26] Borromeo M and Marchesoni F 2007 Phys. Rev. E 75 041106
[27] Roxin A, Brunel N and Hansel D 2005 Phys. Rev. Lett. 94 238103
[28] Wang Q Y, Perc M, Duan Z S and Chen G R 2009 Phys. Rev. E 80 026206
[29] Banerjee T, Biswas D and Sarkar BC 2013 Nonlinear Dyn. 71 279
[30] Banerjee T and Biswas D 2013 Nonlinear Dyn. 73 2025
[31] Banerjee T, Biswas D and Sarkar BC 2013 Nonlinear Dyn. 72 321
[32] Wang F, Zhang C and Li L 2023 Commun. Nonlinear Sci. Numer. Simulat. 126 107447
[33] Stamova I, Stamov G and Li XD 2023 Fractal Fract. 7 845
[34] Lin L F, Lin T Z, Zhang R Q and Wang H Q 2023 Chaos, Solitons and Fractals 170 113406
[35] Yu T, Zhang L, Ji YD and Lai L 2019 Commun. Nonlinear Sci. Numer. Simulat. 72 26
[36] Yan Z, Guirao J L G, Saeed T and Liu X B 2022 Nonlinear Dyn. 110 1233
[37] Zhang G C and Li J H 2010 Commun. Theor. Phys. 53 303
[38] Fang Y W, Luo Y and Zeng C 2022 Chaos, Solitons and Fractals 155 111775
[39] He L F 2023 Phys. Scr. 98 035207
[40] Shapiro V E and Loginov V M 1978 Physica A 91 563
[41] Kempfle S, Schafer I and Beyer H 2002 Nonlinear Dyn. 29 99
[42] Guillouzic S, L’Heureux I and Longtin A 1999 Phys. Rev. E 59 3970
[43] Kim C, Lee E K and Talkner P 2006 Phys. Rev. E 73 026101

Effects of potential field delay and coupling delay on collective behavior of a fractional-order coupled system in a dichotomous fluctuating potential

Effects of potential field delay and coupling delay on collective behavior of a fractional-order coupled system in a dichotomous fluctuating potential

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