Phase-response synchronization in neuronal population

In this study, we have formulated the phase description of the neuronal oscillator with non-instantaneous synaptic inputs and external periodic stimulus by using the phase sensitivity function. By numerical simulation, we have found that the phase of a neuronal oscillator undergoes periodic evolution or locked state, which is determined by the synaptic time constant. The synaptic time constant is also an important condition under which the global network is synchronized. When the synaptic time constant is relatively small, perfectly synchronized behavior quickly occurs in the neuronal population. As the synaptic time constant becomes slightly larger, periodic synchronization emerges in the neuronal population. However, synchronized activity in the neuronal population is lost for larger synaptic time constant. The external periodic stimulus can change the synchronization patterns in the neuronal population. With a weak low-frequency stimulus, the neuronal populations quick synchronized bursting; whereas a high-frequency stimulus can produce synchronized overlapping bursting. We have also found that neuronal oscillators with type-II phase response curves are more susceptible to synchronization than those with type-I phase response curves.