Synchronization and clustering in a nonlinear neural
oscillator network based on physiological models
S. Kim 
, H.T. Kook 
and S.G. Lee
Nonlinear and Complex Systems Lab.,
Dept. Physics, POSTECH, Pohang, Korea 790-784;
Dept. Physics, Kyongwon University,
Sungnam, Seoul, Korea 461-701
Collective dynamics of a network of nonlinear neural oscillators that are coupled globally by synapses has been studied by numerical simulations, phase model analysis, and bifurcation analysis [1]. A variety of phase states including a synchronous state, an anti-phase state, clustered states, and, for strong coupling, exotic complex phase states have been found. A globally coupled network of physiological neuron models such as the Hodgkin-Huxley neurons [2] has been studied with a focus on the transitions among these phase states, in particular, one involving the synchrony. For a variety of coupling geometry and configurations, phase diagrams are constructed in the synaptic parameter space of the reversal potential, the coupling strength, and the propagation time delay. In the weak coupling limit the computed phase diagrams are found to be consistent with the results of analysis using phase models [3]. We have also found that collective dynamics of a network of a large number of neurons is emulated very well by a mesoscopic network with a few neurons, to which bifurcation analysis and the theory of coupled oscillations have been successfully applied to yield comprehensive understanding of the phase dynamics and the phase diagram [4]. The bifurcation analysis shows that there is a transition between the synchrony and the clustered anti-phase states as the time delay is varied and that the phase model predictions break down at some critical value of the coupling strength yielding new complex dynamics. We also explore the effect of the randomness in synaptic parameters on the transitions involving the synchrony. We end with discussions on implications of our findings in modeling cortical dynamics [5].