IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v157y2022ics0960077922001576.html
   My bibliography  Save this article

Phase-locking in k-partite networks of delay-coupled oscillators

Author

Listed:
  • Singha, Joydeep
  • Ramaswamy, Ramakrishna

Abstract

We examine the dynamics of an ensemble of phase oscillators that are divided in k sets, with time-delayed coupling interactions only between oscillators in different sets or partitions. The network of interactions thus forms a k−partite graph. A variety of phase-locked states are observed; these include, in addition to the fully synchronized in-phase solution, splay cluster solutions in which all oscillators within a partition are synchronised and the phase differences between oscillators in different partitions are integer multiples of 2π/k. Such solutions exist independent of the delay and we determine the generalised stability criteria for the existence of these phase-locked solutions. With increase in time-delay, there is an increase in multistability, the generic solutions coexisting with a number of other partially synchronized solutions. The Ott-Antonsen ansatz is applied for the special case of a symmetric k−partite graph to obtain a single time-delayed differential equation for the attracting synchronization manifold. Agreement with numerical results for the specific case of oscillators on a tripartite lattice (the k=3 case) is excellent.

Suggested Citation

  • Singha, Joydeep & Ramaswamy, Ramakrishna, 2022. "Phase-locking in k-partite networks of delay-coupled oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
  • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001576
    DOI: 10.1016/j.chaos.2022.111947
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922001576
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2022.111947?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Serguei Saavedra & Felix Reed-Tsochas & Brian Uzzi, 2009. "A simple model of bipartite cooperation for ecological and organizational networks," Nature, Nature, vol. 457(7228), pages 463-466, January.
    2. Umeshkanta Singh Thounaojam, 2021. "Coarse graining the dynamics of delayed phase oscillators on Cayley trees by star networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-8, January.
    3. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    4. Zhang, Chunmei & Shi, Lin, 2021. "Graph-theoretic method on the periodicity of coupled predator–prey systems with infinite delays on a dispersal network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    5. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yang, Hyeonchae & Jung, Woo-Sung, 2016. "Structural efficiency to manipulate public research institution networks," Technological Forecasting and Social Change, Elsevier, vol. 110(C), pages 21-32.
    2. Yao, Jialing & Sun, Bingbin & Xi, lifeng, 2019. "Fractality of evolving self-similar networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 211-216.
    3. Laurienti, Paul J. & Joyce, Karen E. & Telesford, Qawi K. & Burdette, Jonathan H. & Hayasaka, Satoru, 2011. "Universal fractal scaling of self-organized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3608-3613.
    4. Prasanna Gai & Sujit Kapadia, 2011. "A Network Model of Super-Systemic Crises," Central Banking, Analysis, and Economic Policies Book Series, in: Rodrigo Alfaro (ed.),Financial Stability, Monetary Policy, and Central Banking, edition 1, volume 15, chapter 13, pages 411-432, Central Bank of Chile.
    5. Selen Onel & Abe Zeid & Sagar Kamarthi, 2011. "The structure and analysis of nanotechnology co-author and citation networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 89(1), pages 119-138, October.
    6. Qingmin Hao & Jim Huangnan Shen & Chien-Chiang Lee, 2023. "Risk contagion of bank-firm loan network: evidence from China," Eurasian Business Review, Springer;Eurasia Business and Economics Society, vol. 13(2), pages 341-361, June.
    7. Kashyap, G. & Ambika, G., 2019. "Link deletion in directed complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 631-643.
    8. Gordana Apic & Matthew J Betts & Robert B Russell, 2011. "Content Disputes in Wikipedia Reflect Geopolitical Instability," PLOS ONE, Public Library of Science, vol. 6(6), pages 1-5, June.
    9. Ying Duan & Xiuwen Fu & Wenfeng Li & Yu Zhang & Giancarlo Fortino, 2017. "Evolution of Scale-Free Wireless Sensor Networks with Feature of Small-World Networks," Complexity, Hindawi, vol. 2017, pages 1-15, July.
    10. Gao, Bo & Deng, Zhenghong & Zhao, Dawei, 2016. "Competing spreading processes and immunization in multiplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 175-181.
    11. Li, Xin-Feng & Lu, Zhe-Ming, 2016. "Optimizing the controllability of arbitrary networks with genetic algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 422-433.
    12. Sun, Peng Gang & Che, Wanping & Quan, Yining & Wang, Shuzhen & Miao, Qiguang, 2022. "Random networks are heterogeneous exhibiting a multi-scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    13. Milena Oehlers & Benjamin Fabian, 2021. "Graph Metrics for Network Robustness—A Survey," Mathematics, MDPI, vol. 9(8), pages 1-48, April.
    14. Bokwon Lee & Kyu-Min Lee & Jae-Suk Yang, 2019. "Network structure reveals patterns of legal complexity in human society: The case of the Constitutional legal network," PLOS ONE, Public Library of Science, vol. 14(1), pages 1-15, January.
    15. Johan Rose Santos & Nur Diana Safitri & Maya Safira & Varun Varghese & Makoto Chikaraishi, 2021. "Road network vulnerability and city-level characteristics: A nationwide comparative analysis of Japanese cities," Environment and Planning B, , vol. 48(5), pages 1091-1107, June.
    16. Jianxi Gao & Xueming Liu & Daqing Li & Shlomo Havlin, 2015. "Recent Progress on the Resilience of Complex Networks," Energies, MDPI, vol. 8(10), pages 1-24, October.
    17. Modjtaba Ghorbani & Matthias Dehmer & Frank Emmert-Streib, 2020. "Properties of Entropy-Based Topological Measures of Fullerenes," Mathematics, MDPI, vol. 8(5), pages 1-23, May.
    18. Sara Meerow & Joshua P. Newell, 2015. "Resilience and Complexity: A Bibliometric Review and Prospects for Industrial Ecology," Journal of Industrial Ecology, Yale University, vol. 19(2), pages 236-251, April.
    19. Zhang, Jianhua & Zhao, Mingwei & Liu, Haikuan & Xu, Xiaoming, 2013. "Networked characteristics of the urban rail transit networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1538-1546.
    20. August Hämmerli & Regula Gattiker & Reto Weyermann, 2006. "Conflict and Cooperation in an Actors' Network of Chechnya Based on Event Data," Journal of Conflict Resolution, Peace Science Society (International), vol. 50(2), pages 159-175, April.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001576. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.