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Chimera states in neuronal networks with time delay and electromagnetic induction

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Abstract

Chimera state has been well studied in last decade, and a diversity of chimera states have been revealed in different systems. Recently, its attention has been moved to the neuronal systems, with the purpose of understanding the mechanisms of some brain functions. However, there is no work so far to study the influence of electromagnetic induction on chimera states, which is always with neuronal activities. We here study how the electromagnetic induction influences the chimera states of neuronal networks, especially when it is functioning with the time delay together. We find that for an isolated neuron, the increase in the strength of electromagnetic induction will reduce its firing rate but increase the amplitude of its membrane potential. For a neuronal network, either the time delay or electromagnetic induction can induce chimera states. While their cooperation will result in the robustness of chimera states. This finding may be expected in experiments.

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Acknowledgements

This work was partially supported by the NNSF of China under Grant Nos. 11375066 and 11675056, the NSF of Guizhou Province Education Department under Grant No. KY[2014]316, and the French government under the Paris Seine Initiative.

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Authors and Affiliations

  1. Department of Physics, East China Normal University, Shanghai, 200241, China

    Changhai Tian, Liang Cao, Hongjie Bi, Kesheng Xu & Zonghua Liu

  2. School of Data Science, Tongren University, Tongren, 554300, China

    Changhai Tian

  3. Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, 95302, Cergy-Pontoise Cedex, France

    Hongjie Bi

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  1. Changhai Tian
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Correspondence to Changhai Tian or Zonghua Liu.

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Tian, C., Cao, L., Bi, H. et al. Chimera states in neuronal networks with time delay and electromagnetic induction. Nonlinear Dyn 93, 1695–1704 (2018). https://doi.org/10.1007/s11071-018-4285-z

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