Phase-response Synchronization In Neuronal Population

The phase response curve successfully illuminated how an external stimulus affectsthe timing of spikes immediately after the stimulus in repetitively firing neurons. Thephase response curve also describes the phase shift of the perturbed neuronal oscillatorwhen a neuronal oscillator receives external stimulus or synaptic input. In the presentstudy, we have formulated the phase description of the neuronal oscillator withnon-instantaneous synaptic inputs and external periodic stimulus by using the phasesensitivity function. By numerical simulation, we have found that the phase of aneuronal oscillator undergoes periodic evolution or locked state, which is determined bythe synaptic time constant. The synaptic time constant is also an important conditionunder which the global network synchronized. If the synaptic time constant is relativelysmall, perfectly synchronized behavior quickly occurs in the population of neuronaloscillators. If the synaptic time constant is slightly larger, periodic synchronizationemerges in the population of neuronal oscillators. However, synchronized activity in theneuronal population is lost for larger synaptic time constant. The external periodicstimulation can change the synchronized patterns in the neuronal population. With aweak low-frequency stimulation, the neuronal population quickly tend to synchronizedbursting; a high-frequency stimulation can produce synchronized overlapping bursting.The shape of the PRC plays an important role in determining whether coupled neuronsare able to synchronize both in models and in experimentally manipulated neurons.Herewe have found that neuronal oscillators with type-II phase response curves are moresusceptible to synchronize than those with type-I phase response curves.The synapsescan produce inhibitory postsynaptic potential or excitatory postsynaptic potential underthe input signal.In this paper, we have found that excitatory synaptic input can causeneural oscillator smooth volatility associated with synaptic time constant. In addition,under excitatory and inhibitory synapses input, we have found that inhibitory synapticinput can reduce the period of neural oscillator and the degree of synchronization in theneuronal population.