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Synchronization of "Hopf/homoclinic" bursting with "SubHopf/homoclinic" bursting

Wang Fu-Xia Xie Yong

Synchronization of "Hopf/homoclinic" bursting with "SubHopf/homoclinic" bursting

Wang Fu-Xia, Xie Yong
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  • Abstract views:  862
  • PDF Downloads:  489
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  • Received Date:  18 June 2012
  • Accepted Date:  30 July 2012
  • Published Online:  20 January 2013

Synchronization of "Hopf/homoclinic" bursting with "SubHopf/homoclinic" bursting

  • 1. State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 10972170, 11272241).

Abstract: Taking the modified Morris-Lecar neuron model for example, we consider the synchronous behaviour between "Hopf/homoclinic" bursting and "SubHopf/homoclinic" bursting. Firstly, the synchronization between two coupled bursting neurons with the same topological type is investigated numerically, and the results show that the coupling strength reaching the synchronization of the membrane potential of "Hopf/homoclinic" bursting is smaller than that of "SubHopf/homoclinic" bursting, that is to say, the former can reach complete synchrony of the membrane potential more easily than the latter. Secondly, we study the synchronous behavior of two coupled bursting neurons with different topological types by numerical analysis, and find that with the increase of the coupling strength the two different types of bursting neurons reach the bursting-synchrony first, and then they can reach complete synchrony of the membrane potential when the coupling strength is strong enough, and the type of synchronous state is inclined to the type of easy synchronization, namely, "Hopf/homoclinic" bursting. To our surprise, the slow variables exhibit phase synchronization instead of complete synchronization. Moreover, there is a linear relationship between the both slow variables. This point is distinctly different from the results of the existing documents.

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