IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v144y2021ics096007792100045x.html
   My bibliography  Save this article

Patterns in coupled FitzHugh–Nagumo model on duplex networks

Author

Listed:
  • Lei, Lixing
  • Yang, Junzhong

Abstract

Patterns out of homogeneous equilibrium on monolayer networks have been well-documented. However, it is a challenge to understand patterns on multiplex networks. In this work, we study coupled FitzHugh–Nagumo model on duplex networks consisting of two layers. By numerical investigations, we find that the emergent patterns may be characterized by dominant network modes when the homogeneous equilibrium becomes unstable. These dominant network modes on duplex networks are related to the most unstable network modes in monolayer networks. Using these dominant networks modes, we develop approximation methods to deal with the instability of the homogeneous equilibrium on duplex networks. The comparison between theoretical and numerical results suggests that the approximation methods may serve as a tool for analyzing patterns on duplex networks.

Suggested Citation

  • Lei, Lixing & Yang, Junzhong, 2021. "Patterns in coupled FitzHugh–Nagumo model on duplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s096007792100045x
    DOI: 10.1016/j.chaos.2021.110692
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792100045X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110692?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. Dorogovtsev, S. N. & Mendes, J.F.F., 2013. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780199686711.
    2. Han, Wenchen & Yang, Junzhong, 2018. "Approximation methods for the stability analysis of complete synchronization on duplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 23-27.
    3. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    4. Zanin, Massimiliano, 2015. "Can we neglect the multi-layer structure of functional networks?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 184-192.
    5. Lü, Jinhu & Yu, Xinghuo & Chen, Guanrong, 2004. "Chaos synchronization of general complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 281-302.
    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. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Global synchronization in general complex delayed dynamical networks and its applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 729-742.
    2. Fei Wang & Zhaowen Zheng & Yongqing Yang, 2019. "Synchronization of Complex Dynamical Networks with Hybrid Time Delay under Event-Triggered Control: The Threshold Function Method," Complexity, Hindawi, vol. 2019, pages 1-17, December.
    3. Qian Liu & Wenchen Han & Lixing Lei & Qionglin Dai & Junzhong Yang, 2019. "Chaos Synchronization in Time-Dependent Duplex Networks," Complexity, Hindawi, vol. 2019, pages 1-8, April.
    4. Liu, Xiwei & Chen, Tianping, 2007. "Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 82-92.
    5. Nicanor García Álvarez & Belarmino Adenso-Díaz & Laura Calzada-Infante, 2021. "Maritime Traffic as a Complex Network: a Systematic Review," Networks and Spatial Economics, Springer, vol. 21(2), pages 387-417, June.
    6. Liu, Tao & Dimirovski, Georgi M. & Zhao, Jun, 2008. "Exponential synchronization of complex delayed dynamical networks with general topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 643-652.
    7. Yang, Li-xin & Jiang, Jun, 2018. "Synchronization analysis of fractional order drive-response networks with in-commensurate orders," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 47-52.
    8. Lu, Jianquan & Ho, Daniel W.C., 2008. "Local and global synchronization in general complex dynamical networks with delay coupling," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1497-1510.
    9. Rybalova, E.V. & Strelkova, G.I. & Anishchenko, V.S., 2021. "Impact of sparse inter-layer coupling on the dynamics of a heterogeneous multilayer network of chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    10. He, Guangming & Yang, Jingyu, 2008. "Adaptive synchronization in nonlinearly coupled dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1254-1259.
    11. Yang, Yong & Tu, Lilan & Li, Kuanyang & Guo, Tianjiao, 2019. "Optimized inter-structure for enhancing the synchronizability of interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 310-318.
    12. Wu, Jianshe & Jiao, Licheng, 2007. "Synchronization in complex delayed dynamical networks with nonsymmetric coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 513-530.
    13. Du, Hongyue, 2011. "Function projective synchronization in drive–response dynamical networks with non-identical nodes," Chaos, Solitons & Fractals, Elsevier, vol. 44(7), pages 510-514.
    14. Guan, Zhi-Hong & Zhang, Hao, 2008. "Stabilization of complex network with hybrid impulsive and switching control," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1372-1382.
    15. Li, Ping & Yi, Zhang & Zhang, Lei, 2006. "Global synchronization of a class of delayed complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 903-908.
    16. Wu, Jianshe & Jiao, Licheng, 2007. "Observer-based synchronization in complex dynamical networks with nonsymmetric coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 469-480.
    17. Lucas Cuadra & Sancho Salcedo-Sanz & Javier Del Ser & Silvia Jiménez-Fernández & Zong Woo Geem, 2015. "A Critical Review of Robustness in Power Grids Using Complex Networks Concepts," Energies, MDPI, vol. 8(9), pages 1-55, August.
    18. Liu, Tao & Zhao, Jun & Hill, David J., 2009. "Synchronization of complex delayed dynamical networks with nonlinearly coupled nodes," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1506-1519.
    19. Zhou, Jin & Lu, Jun-an, 2007. "Topology identification of weighted complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 481-491.
    20. Wu, Xiaoqun, 2008. "Synchronization-based topology identification of weighted general complex dynamical networks with time-varying coupling delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 997-1008.

    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:144:y:2021:i:c:s096007792100045x. 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.