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Complete synchronization of coupled Rulkov neuron networks

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Abstract

Based on the master stability function (MSF) analysis, the complete synchronization of coupled chaotic Rulkov neuron networks is investigated in detail. The two-dimensional parameter-space plots that display directly the values of the MSF in different colors are numerically obtained. For the electrical coupled Rulkov neuron network, the values of MSF are all positive when the single Rulkov neuron is in chaotic bursting state or spiking state, which means that complete synchronization of the electrical coupled Rulkov neuron network can not attain. Importantly, a specific inner linking function is found to make the values of the MSF negative, which means that the necessary condition of complete synchronization is satisfied. Through numerical simulations, the existence of complete synchronization is verified for Rulkov neuron network with the very specific inner linking function that has been employed. In addition, the number of nodes of networks and the explicit thresholds for the coupling strength that guarantees the necessary condition of complete synchronization are derived in three typical regular networks. More interestingly, the same route of spatiotemporal patterns transition is found for Rulkov neurons in three typical regular networks.

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Acknowledgments

This work is supported by the Natural Science Foundation of China (NSFC) under Project No. 11171017 and the Fundamental Research Funds for the Central Universities under Project No. 2015YJS175.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Huijing Sun & Hongjun Cao

  2. Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University, Yantai, 264001, Shandong, People’s Republic of China

    Huijing Sun

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  1. Huijing Sun
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  2. Hongjun Cao
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Correspondence to Hongjun Cao.

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Sun, H., Cao, H. Complete synchronization of coupled Rulkov neuron networks. Nonlinear Dyn 84, 2423–2434 (2016). https://doi.org/10.1007/s11071-016-2654-z

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  • DOI: https://doi.org/10.1007/s11071-016-2654-z

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