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

Author

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  • 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
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Wang, Qingyun & Zheng, Yanhong & Ma, Jun, 2013. "Cooperative dynamics in neuronal networks," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 19-27.
    14. 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).
    15. 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.
    16. 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.
    17. 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).
    18. 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.
    19. 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.
    20. Kyungjin Yoo & Seth Blumsack, 2018. "The Political Complexity of Regional Electricity Policy Formation," Complexity, Hindawi, vol. 2018, pages 1-18, December.
    21. 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.

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