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 t...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.展开更多
This paper studies a dynamical model of electroencephalogram(EEG).By linearizing the EEG model conditions for the stability of equilibrium point are obtained. Choosing excitatory inputs as bifurcation parameters, nume...This paper studies a dynamical model of electroencephalogram(EEG).By linearizing the EEG model conditions for the stability of equilibrium point are obtained. Choosing excitatory inputs as bifurcation parameters, numerical simulations show that the EEG model exhibits a series of complex dynamics, including limit cycle,periodic doubling bifurcation, periodic halving bifurcation, chaotic bands with periodic windows.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10872014 and 10802012)the Development Foundation of Science of Nanjing University of Science and Technology (Grant No.XKF09036)
文摘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.
基金Scientific Research Fund of Liaoning Provincial Education Department
文摘This paper studies a dynamical model of electroencephalogram(EEG).By linearizing the EEG model conditions for the stability of equilibrium point are obtained. Choosing excitatory inputs as bifurcation parameters, numerical simulations show that the EEG model exhibits a series of complex dynamics, including limit cycle,periodic doubling bifurcation, periodic halving bifurcation, chaotic bands with periodic windows.
