IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i17p2135-d627801.html
   My bibliography  Save this article

Relay Synchronization in a Weighted Triplex Network

Author

Listed:
  • Md Sayeed Anwar

    (Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India)

  • Dibakar Ghosh

    (Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India)

  • Nikita Frolov

    (Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 420500 Innopolis, Russia
    Center for Neurotechnology and Machine Learning, Immanuel Kant Baltic Federal University, 236041 Kaliningrad, Russia)

Abstract

Relay synchronization in multi-layer networks implies inter-layer synchronization between two indirectly connected layers through a relay layer. In this work, we study the relay synchronization in a three-layer multiplex network by introducing degree-based weighting mechanisms. The mechanism of within-layer connectivity may be hubs-repelling or hubs-attracting whenever low-degree or high-degree nodes receive strong influence. We adjust the remote layers to hubs-attracting coupling, whereas the relay layer may be unweighted, hubs-repelling, or hubs-attracting network. We establish that relay synchronization is improved when the relay layer is hubs-repelling compared to the other cases. We determine analytically necessary stability conditions of relay synchronization state using the master stability function approach. Finally, we explore the relation between synchronization and the topological property of the relay layer. We find that a higher clustering coefficient hinders synchronizability, and vice versa. We also look into the intra-layer synchronization in the proposed weighted triplex network and establish that intra-layer synchronization occurs in a wider range when relay layer is hubs-attracting.

Suggested Citation

  • Md Sayeed Anwar & Dibakar Ghosh & Nikita Frolov, 2021. "Relay Synchronization in a Weighted Triplex Network," Mathematics, MDPI, vol. 9(17), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2135-:d:627801
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/17/2135/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/17/2135/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Frolov, Nikita & Rakshit, Sarbendu & Maksimenko, Vladimir & Kirsanov, Daniil & Ghosh, Dibakar & Hramov, Alexander, 2021. "Coexistence of interdependence and competition in adaptive multilayer network," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Clemente, G.P. & Grassi, R., 2018. "Directed clustering in weighted networks: A new perspective," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 26-38.
    3. Anwar, Md Sayeed & Kundu, Srilena & Ghosh, Dibakar, 2021. "Enhancing synchrony in asymmetrically weighted multiplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Fabio Rossa & Louis Pecora & Karen Blaha & Afroza Shirin & Isaac Klickstein & Francesco Sorrentino, 2020. "Symmetries and cluster synchronization in multilayer networks," Nature Communications, Nature, vol. 11(1), pages 1-17, December.
    5. Vadivel, R. & Hammachukiattikul, P. & Gunasekaran, Nallappan & Saravanakumar, R. & Dutta, Hemen, 2021. "Strict dissipativity synchronization for delayed static neural networks: An event-triggered scheme," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. Christel Kamp & Mathieu Moslonka-Lefebvre & Samuel Alizon, 2013. "Epidemic Spread on Weighted Networks," PLOS Computational Biology, Public Library of Science, vol. 9(12), pages 1-10, December.
    7. Frolov, Daniil, 2018. "Эво-Дево: Парадигмальный Вызов Для Институционально-Эволюционного Анализа (Версия 2.0) [Evo-Devo: Paradigmal Challenge for Institutional-Evolutionary Analysis (version 2.0)]," MPRA Paper 90285, University Library of Munich, Germany.
    8. Lu, Xin Biao & Wang, Xiao Fan & Li, Xiang & Fang, Jin Qing, 2006. "Synchronization in weighted complex networks: Heterogeneity and synchronizability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 381-389.
    9. Kevin McCann & Alan Hastings & Gary R. Huxel, 1998. "Weak trophic interactions and the balance of nature," Nature, Nature, vol. 395(6704), pages 794-798, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pal, Palash Kumar & Bhowmick, Sourav K. & Karmakar, Partha & Ghosh, Dibakar, 2023. "Mixed synchronization in multiplex networks of counter-rotating oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

    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. Anwar, Md Sayeed & Kundu, Srilena & Ghosh, Dibakar, 2021. "Enhancing synchrony in asymmetrically weighted multiplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Panayotis Christidis & Álvaro Gomez Losada, 2019. "Email Based Institutional Network Analysis: Applications and Risks," Social Sciences, MDPI, vol. 8(11), pages 1-14, November.
    3. Tinic, Murat & Sensoy, Ahmet & Demir, Muge & Nguyen, Duc Khuong, 2020. "Broker Network Connectivity and the Cross-Section of Expected Stock Returns," MPRA Paper 104719, University Library of Munich, Germany.
    4. Christophe Chorro & Emmanuelle Jay & Philippe De Peretti & Thibault Soler, 2021. "Frequency causality measures and Vector AutoRegressive (VAR) models: An improved subset selection method suited to parsimonious systems," Documents de travail du Centre d'Economie de la Sorbonne 21013, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Roy Cerqueti & Francesca Pampurini & Annagiulia Pezzola & Anna Grazia Quaranta, 2022. "Dangerous liasons and hot customers for banks," Review of Quantitative Finance and Accounting, Springer, vol. 59(1), pages 65-89, July.
    6. Sun, Meng & Zhuang, Guangming & Xia, Jianwei & Wang, Yanqian & Chen, Guoliang, 2022. "Stochastic admissibility and H∞ output feedback control for singular Markov jump systems under dynamic measurement output event-triggered strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    7. Dai, Chuanjun & Zhao, Min & Chen, Lansun, 2012. "Complex dynamic behavior of three-species ecological model with impulse perturbations and seasonal disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 84(C), pages 83-97.
    8. Rosanna Grassi & Paolo Bartesaghi & Stefano Benati & Gian Paolo Clemente, 2021. "Multi-Attribute Community Detection in International Trade Network," Networks and Spatial Economics, Springer, vol. 21(3), pages 707-733, September.
    9. George Van Voorn & Geerten Hengeveld & Jan Verhagen, 2020. "An agent based model representation to assess resilience and efficiency of food supply chains," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-27, November.
    10. Dina in ‘t Zandt & Zuzana Kolaříková & Tomáš Cajthaml & Zuzana Münzbergová, 2023. "Plant community stability is associated with a decoupling of prokaryote and fungal soil networks," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
    11. Miehls, Andrea L. Jaeger & Mason, Doran M. & Frank, Kenneth A. & Krause, Ann E. & Peacor, Scott D. & Taylor, William W., 2009. "Invasive species impacts on ecosystem structure and function: A comparison of the Bay of Quinte, Canada, and Oneida Lake, USA, before and after zebra mussel invasion," Ecological Modelling, Elsevier, vol. 220(22), pages 3182-3193.
    12. Yang, Wei & Cui, Guozeng & Ma, Qian & Ma, Jiali & Tao, Chongben, 2022. "Finite-time adaptive event-triggered command filtered backstepping control for a QUAV," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    13. Liu, Haoliang & Zhang, Taixiang & Li, Xiaodi, 2021. "Event-triggered control for nonlinear systems with impulse effects," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    14. Nadia von Jacobi & Vito Amendolagine, 2021. "What Feeds on What? Networks of Interdependencies between Culture and Institutions," DEM Working Papers 2021/13, Department of Economics and Management.
    15. Nguyen, Tung T. & Budzinski, Roberto C. & Pasini, Federico W. & Delabays, Robin & Mináč, Ján & Muller, Lyle E., 2023. "Broadcasting solutions on networked systems of phase oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    16. Christophe Chorro & Emmanuelle Jay & Philippe de Peretti & Thibault Soler, 2021. "Frequency causality measures and Vector AutoRegressive (VAR) models: An improved subset selection method suited to parsimonious systems," Post-Print halshs-03216938, HAL.
    17. Christopher C Wilmers & Wayne M Getz, 2005. "Gray Wolves as Climate Change Buffers in Yellowstone," PLOS Biology, Public Library of Science, vol. 3(4), pages 1-1, March.
    18. Scotti, Marco & Bondavalli, Cristina & Bodini, Antonio, 2009. "Linking trophic positions and flow structure constraints in ecological networks: Energy transfer efficiency or topology effect?," Ecological Modelling, Elsevier, vol. 220(21), pages 3070-3080.
    19. Chun-Wei Chang & Takeshi Miki & Hao Ye & Sami Souissi & Rita Adrian & Orlane Anneville & Helen Agasild & Syuhei Ban & Yaron Be’eri-Shlevin & Yin-Ru Chiang & Heidrun Feuchtmayr & Gideon Gal & Satoshi I, 2022. "Causal networks of phytoplankton diversity and biomass are modulated by environmental context," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    20. Hartvig, Martin & Andersen, Ken Haste, 2013. "Coexistence of structured populations with size-based prey selection," Theoretical Population Biology, Elsevier, vol. 89(C), pages 24-33.

    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:gam:jmathe:v:9:y:2021:i:17:p:2135-:d:627801. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.