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Firing properties and synchronization rate in fractional-order Hindmarsh-Rose model neurons

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  • Special Topic: Neurodynamics
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Abstract

We find that the fractional-order Hindmarsh-Rose model neuron demonstrates various types of firing behavior as a function of the fractional order in this study. There exists a clear difference in the bifurcation diagram between the fractional-order Hindmarsh-Rose model and the corresponding integer-order model even though the neuron undergoes a Hopf bifurcation to oscillation and then starts a period-doubling cascade to chaos with the decrease of the externally applied current. Interestingly, the discharge frequency of the fractional-order Hindmarsh-Rose model neuron is greater than that of the integer-order counterpart irrespective of whether the neuron exhibits periodic or chaotic firing. Then we demonstrate that the firing behavior of the fractional-order Hindmarsh-Rose model neuron has a higher complexity than that of the integer-order counterpart. Also, the synchronization phenomenon is investigated in the network of two electrically coupled fractional-order model neurons. We show that the synchronization rate increases as the fractional order decreases.

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Authors and Affiliations

  1. State Key Lab of Strength and Vibration for Mechanical Structures, Xi’an Jiaotong University, Xi’an, 710049, China

    Yong Xie, Yong Liu & Ying Wu

  2. School of Mathematics and Stastics, Xi’an Jiaotong University, Xi’an, 710049, China

    YanMei Kang

Authors
  1. Yong Xie
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  2. YanMei Kang
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  3. Yong Liu
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  4. Ying Wu
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Correspondence to Yong Xie.

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Xie, Y., Kang, Y., Liu, Y. et al. Firing properties and synchronization rate in fractional-order Hindmarsh-Rose model neurons. Sci. China Technol. Sci. 57, 914–922 (2014). https://doi.org/10.1007/s11431-014-5531-3

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  • DOI: https://doi.org/10.1007/s11431-014-5531-3

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