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 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 synchronousregimes in coupled neurons because different regimes may correspondto different cognitive and pathological states. In this paper, phasesynchronization and its transitions are discussed by means oftheoretical and numerical analyses. In two coupled modifiedMorris--Lecar neurons with a gap junction, we show that the occurrenceof phase synchronization can be investigated from the dynamics ofphase equation, and the analytical synchronization condition isderived. By defining the phase of spike and burst, the transitionsfrom burst synchronization to spike synchronization and then towardnearly complete synchronization can be identified by bifurcationdiagrams, the mean frequency difference and time series of neurons.The simulation results suggest that the synchronization of burstingactivity is a multi-time-scale phenomenon and the phasesynchronization deduced by the phase equation is actually spikesynchronization. |
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Keywords: | phase synchronization synchronization transition bifurcation diagram |
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