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Collective dynamics of fluctuating–damping coupled oscillators in network structures: Stability, synchronism, and resonant behaviors

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  • Zhang, Ruoqi
  • Meng, Lin
  • Yu, Lei
  • Shi, Sihong
  • Wang, Huiqi

Abstract

The investigation of collective behaviors and synergies in coupled systems holds great significance in many fields. In this paper, we propose the coupled system of overdamped fluctuating–damping oscillators in a general network framework. Our initial theoretical analysis focuses on the system’s synchronization and stability, revealing that both the first and second moments of the mean field are asymptotic stability, and the system exhibits a property of stochastic asymptotic synchronization with the mean field, irrespective of coupled structures. Furthermore, we explore the system’s collective behaviors by analyzing the output amplitude amplification (OAA), where we observe the emergence of generalized stochastic resonance (GSR) phenomena. Finally, we numerically verify the influence of system parameters on stability and synchronization in different coupled structures by introducing the mean first stability time and mean first synchronization time in the simulations. Our findings indicate that the structure does not significantly influence the system stability, whereas it does play a synergistic role in influencing the synchronization. Moreover, we further extend the investigation in complex networks, and observe the non-monotonous phenomena of mean first synchronization time varying with the heterogeneity.

Suggested Citation

  • Zhang, Ruoqi & Meng, Lin & Yu, Lei & Shi, Sihong & Wang, Huiqi, 2024. "Collective dynamics of fluctuating–damping coupled oscillators in network structures: Stability, synchronism, and resonant behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 638(C).
    • Handle: RePEc:eee:phsmap:v:638:y:2024:i:c:s0378437124001365
    DOI: 10.1016/j.physa.2024.129628
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    1. Vishwamittar, & Batra, Priyanka & Chopra, Ribhu, 2021. "Stochastic resonance in two coupled fractional oscillators with potential and coupling parameters subjected to quadratic asymmetric dichotomous noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    2. Spagnolo, B. & Valenti, D. & Guarcello, C. & Carollo, A. & Persano Adorno, D. & Spezia, S. & Pizzolato, N. & Di Paola, B., 2015. "Noise-induced effects in nonlinear relaxation of condensed matter systems," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 412-424.
    3. Simon Gross & Christoph Barmet & Benjamin E. Dietrich & David O. Brunner & Thomas Schmid & Klaas P. Pruessmann, 2016. "Dynamic nuclear magnetic resonance field sensing with part-per-trillion resolution," Nature Communications, Nature, vol. 7(1), pages 1-7, December.
    4. Gao, Shilong & Gao, Nunan & Kan, Bixia & Wang, Huiqi, 2021. "Stochastic resonance in coupled star-networks with power-law heterogeneity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    5. He, Guitian & Guo, Dali & Tian, Yan & Li, Tiejun & Luo, Maokang, 2017. "Mittag-Leffler noise induced stochastic resonance in a generalized Langevin equation with random inherent frequency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 91-103.
    6. G. Bonanno & D. Valenti & B. Spagnolo, 2005. "Role of Noise in a Market Model with Stochastic Volatility," Papers cond-mat/0510154, arXiv.org, revised Oct 2006.
    7. Lin, Lifeng & He, Minyue & Wang, Huiqi, 2022. "Collective resonant behaviors in two coupled fluctuating-mass oscillators with tempered Mittag-Leffler memory kernel," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    8. Lv, Wangyong & Wang, Huiqi & Lin, Lifeng & Wang, Fei & Zhong, Suchuan, 2015. "Transport properties of elastically coupled fractional Brownian motors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 149-161.
    9. Ren, Ruibin & Deng, Ke, 2019. "Noise and periodic signal induced stochastic resonance in a Langevin equation with random mass and frequency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 145-155.
    10. Betül Kalaycı & Ayşe Özmen & Gerhard-Wilhelm Weber, 2020. "Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS," Annals of Operations Research, Springer, vol. 295(1), pages 183-206, December.
    11. Tian, Yan & Yu, Tao & He, Gui-Tian & Zhong, Lin-Feng & Stanley, H. Eugene, 2020. "The resonance behavior in the fractional harmonic oscillator with time delay and fluctuating mass," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    12. Rzehak, R. & Zimmermann, W., 2003. "Inertial effects in Brownian motion of a trapped particle in shear flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 495-508.
    13. He, Lifang & Wu, Xia & Zhang, Gang, 2020. "Stochastic resonance in coupled fractional-order linear harmonic oscillators with damping fluctuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    14. J. Gómez-Ordóñez & J. Casado & M. Morillo, 2011. "Arrays of noisy bistable elements with nearest neighbor coupling: equilibrium and stochastic resonance," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 82(2), pages 179-187, July.
    15. G. Bonanno & D. Valenti & B. Spagnolo, 2006. "Role of noise in a market model with stochastic volatility," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 53(3), pages 405-409, October.
    16. K. Hennessy & A. Badolato & M. Winger & D. Gerace & M. Atatüre & S. Gulde & S. Fält & E. L. Hu & A. Imamoğlu, 2007. "Quantum nature of a strongly coupled single quantum dot–cavity system," Nature, Nature, vol. 445(7130), pages 896-899, February.
    17. Chen, Xi & Luo, Maokang & Zhong, Yangfan & Zhang, Lu, 2022. "Collective dynamic behaviors of a general adjacent coupled chain in both unconfined and confined spaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    Full references (including those not matched with items on IDEAS)

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