IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i16p3299-3306.html
   My bibliography  Save this article

Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling

Author

Listed:
  • Wang, Qingyun
  • Perc, Matjaž
  • Duan, Zhisheng
  • Chen, Guanrong

Abstract

We study synchronization transitions and pattern formation on small-world networks consisting of Morris–Lecar excitable neurons in dependence on the information transmission delay and the rewiring probability. In addition, networks formed via gap junctional connections and coupling via chemical synapses are considered separately. For gap-junctionally coupled networks we show that short delays can induce zigzag fronts of excitations, whereas long delays can further detriment synchronization due to a dynamic clustering anti-phase synchronization transition. For the synaptically coupled networks, on the other hand, we find that the clustering anti-phase synchronization can appear as a direct consequence of the prolongation of information transmission delay, without being accompanied by zigzag excitatory fronts. Irrespective of the coupling type, however, we show that an appropriate small-world topology can always restore synchronized activity if only the information transmission delays are short or moderate at most. Long information transmission delays always evoke anti-phase synchronization and clustering, in which case the fine-tuning of the network topology fails to restore the synchronization of neuronal activity.

Suggested Citation

  • Wang, Qingyun & Perc, Matjaž & Duan, Zhisheng & Chen, Guanrong, 2010. "Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3299-3306.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:16:p:3299-3306
    DOI: 10.1016/j.physa.2010.03.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711000275X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2010.03.031?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.

    Citations

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


    Cited by:

    1. Deng, Bin & Zhu, Zechen & Yang, Shuangming & Wei, Xile & Wang, Jiang & Yu, Haitao, 2016. "FPGA implementation of motifs-based neuronal network and synchronization analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 388-402.
    2. Zeng, Xiaocai & Xiong, Zuoliang & Wang, Changjian, 2016. "Hopf bifurcation for neutral-type neural network model with two delays," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 17-31.
    3. Yu, Haitao & Guo, Xinmeng & Qin, Qing & Deng, Yun & Wang, Jiang & Liu, Jing & Cao, Yibin, 2017. "Synchrony dynamics underlying effective connectivity reconstruction of neuronal circuits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 674-687.
    4. Sun, Shiwen & Li, Ruiqi & Wang, Li & Xia, Chengyi, 2015. "Reduced synchronizability of dynamical scale-free networks with onion-like topologies," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 249-256.
    5. Hao, Yinghang & Gong, Yubing & Wang, Li & Ma, Xiaoguang & Yang, Chuanlu, 2011. "Single or multiple synchronization transitions in scale-free neuronal networks with electrical or chemical coupling," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 260-268.
    6. Liu, Chen & Wang, Jiang & Yu, Haitao & Deng, Bin & Wei, Xile & Sun, Jianbing & Chen, Yingyuan, 2013. "The effects of time delay on the synchronization transitions in a modular neuronal network with hybrid synapses," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 54-65.
    7. Kim, Sang-Yoon & Lim, Woochang, 2015. "Effect of small-world connectivity on fast sparsely synchronized cortical rhythms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 109-123.
    8. Gequn, Liu & Wenhui, Li & Huijie, Yang & Knowles, Gareth, 2014. "The control gain region for synchronization in non-diffusively coupled complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 17-24.
    9. Wang, Qingyun & Zheng, Yanhong & Ma, Jun, 2013. "Cooperative dynamics in neuronal networks," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 19-27.
    10. Yu, Haitao & Wang, Jiang & Liu, Chen & Deng, Bin & Wei, Xile, 2014. "Delay-induced synchronization transitions in modular scale-free neuronal networks with hybrid electrical and chemical synapses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 25-34.
    11. Rajagopal, Karthikeyan & Jafari, Sajad & Li, Chunbiao & Karthikeyan, Anitha & Duraisamy, Prakash, 2021. "Suppressing spiral waves in a lattice array of coupled neurons using delayed asymmetric synapse coupling," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    12. Kyungjin Yoo & Seth Blumsack, 2018. "The Political Complexity of Regional Electricity Policy Formation," Complexity, Hindawi, vol. 2018, pages 1-18, December.
    13. Li, Jiajia & Wang, Rong & Du, Mengmeng & Tang, Jun & Wu, Ying, 2016. "Dynamic transition on the seizure-like neuronal activity by astrocytic calcium channel block," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 702-708.
    14. Wang, Baoying & Gong, Yubing & Xie, Huijuan & Wang, Qi, 2016. "Optimal autaptic and synaptic delays enhanced synchronization transitions induced by each other in Newman–Watts neuronal networks," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 372-378.
    15. Shi, Peiming & Xia, Haifeng & Han, Dongying & Fu, Rongrong & Yuan, Danzhen, 2018. "Stochastic resonance in a time polo-delayed asymmetry bistable system driven by multiplicative white noise and additive color noise," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 8-14.
    16. Wu, Hao & Jiang, Huijun & Hou, Zhonghuai, 2011. "Spatiotemporal dynamics on small-world neuronal networks: The roles of two types of time-delayed coupling," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 836-844.
    17. Jun Wang & Yongqiang Tian & Lanfeng Hua & Kaibo Shi & Shouming Zhong & Shiping Wen, 2023. "New Results on Finite-Time Synchronization Control of Chaotic Memristor-Based Inertial Neural Networks with Time-Varying Delays," Mathematics, MDPI, vol. 11(3), pages 1-18, January.
    18. Wang, Zhizhi & Hu, Bing & Zhou, Weiting & Xu, Minbo & Wang, Dingjiang, 2023. "Hopf bifurcation mechanism analysis in an improved cortex-basal ganglia network with distributed delays: An application to Parkinson’s disease," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    19. Yu, Haitao & Wang, Jiang & Liu, Chen & Deng, Bin & Wei, Xile, 2013. "Delay-induced synchronization transitions in small-world neuronal networks with hybrid electrical and chemical synapses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5473-5480.
    20. Yu, Haitao & Wang, Jiang & Liu, Qiuxiang & Sun, Jianbing & Yu, Haifeng, 2013. "Delay-induced synchronization transitions in small-world neuronal networks with hybrid synapses," Chaos, Solitons & Fractals, Elsevier, vol. 48(C), pages 68-74.
    21. Suresh, R. & Senthilkumar, D.V. & Lakshmanan, M. & Kurths, J., 2016. "Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 235-245.

    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:phsmap:v:389:y:2010:i:16:p:3299-3306. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.