Nonlinear Dynamics

, Volume 84, Issue 4, pp 2423–2434 | Cite as

Complete synchronization of coupled Rulkov neuron networks

  • Huijing Sun
  • Hongjun Cao
Original Paper


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.


Chaotic Rulkov map-based neuron network Master stability function analysis Inner linking function Network structure Spatiotemporal patterns 



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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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Mathematics, School of ScienceBeijing Jiaotong UniversityBeijingPeople’s Republic of China
  2. 2.Institute of Systems Science and MathematicsNaval Aeronautical and Astronautical UniversityYantaiPeople’s Republic of China

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