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Bifurcation and synchronization of synaptically coupled FHN models with time delay

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  • Wang, Qingyun
  • Lu, Qishao
  • Chen, GuanRong
  • feng, Zhaosheng
  • Duan, LiXia

Abstract

This paper presents an investigation of dynamics of the coupled nonidentical FHN models with synaptic connection, which can exhibit rich bifurcation behavior with variation of the coupling strength. With the time delay being introduced, the coupled neurons may display a transition from the original chaotic motions to periodic ones, which is accompanied by complex bifurcation scenario. At the same time, synchronization of the coupled neurons is studied in terms of their mean frequencies. We also find that the small time delay can induce new period windows with the coupling strength increasing. Moreover, it is found that synchronization of the coupled neurons can be achieved in some parameter ranges and related to their bifurcation transition. Bifurcation diagrams are obtained numerically or analytically from the mathematical model and the parameter regions of different behavior are clarified.

Suggested Citation

  • Wang, Qingyun & Lu, Qishao & Chen, GuanRong & feng, Zhaosheng & Duan, LiXia, 2009. "Bifurcation and synchronization of synaptically coupled FHN models with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 918-925.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:2:p:918-925
    DOI: 10.1016/j.chaos.2007.01.061
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    Citations

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    Cited by:

    1. Gong, Yubing & Xie, Yanhang & Lin, Xiu & Hao, Yinghang & Ma, Xiaoguang, 2010. "Ordering chaos and synchronization transitions by chemical delay and coupling on scale-free neuronal networks," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 96-103.
    2. 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.
    3. Zhang, Qunjiao, 2014. "Robust synchronization of FitzHugh–Nagumo network with parameter disturbances by sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 22-26.
    4. 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.
    5. Gong, Yubing & Wang, Li & Xu, Bo, 2012. "Delay-induced diversity of firing behavior and ordered chaotic firing in adaptive neuronal networks," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 548-553.
    6. Wang, Jing & Ye, Weijie & Liu, Shenquan & Lu, Bo & Jiang, Xiaofang, 2016. "Qualitative and quantitative aspects of synchronization in coupled CA1 pyramidal neurons," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 32-38.
    7. 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.
    8. Wang, Jing & Liu, Shenquan & Liu, Xuanliang, 2014. "Quantification of synchronization phenomena in two reciprocally gap-junction coupled bursting pancreatic β-cells," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 65-71.

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