Phase synchronization and its transition in two coupled bursting neurons: theoretical and numerical analysis |
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| Authors: | Wang Hai-Xi Lu Qi-Shao and Shi Xia |
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| Affiliation: | School of Science, Nanjing University of Science and Technology, Nanjing 210094, China; Department of Dynamics and Control, Beihang University, Beijing 100191, China; School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China |
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| Abstract: | It is crucially important to study different synchronous
regimes in coupled neurons because different regimes may correspond
to different cognitive and pathological states. In this paper, phase
synchronization and its transitions are discussed by means of
theoretical and numerical analyses. In two coupled modified
Morris--Lecar neurons with a gap junction, we show that the occurrence
of phase synchronization can be investigated from the dynamics of
phase equation, and the analytical synchronization condition is
derived. By defining the phase of spike and burst, the transitions
from burst synchronization to spike synchronization and then toward
nearly complete synchronization can be identified by bifurcation
diagrams, the mean frequency difference and time series of neurons.
The simulation results suggest that the synchronization of bursting
activity is a multi-time-scale phenomenon and the phase
synchronization deduced by the phase equation is actually spike
synchronization. |
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| Keywords: | phase synchronization synchronization transition bifurcation diagram |
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