In this paper, we study effects of partial time delays on phase synchronization in Watts-Strogatz small-world neuronal networks. Our focus is on the impact of two parameters, namely the time delay s and the probability of partial time delay p delay , whereby the latter determines the probability with which a connection between two neurons is delayed. Our research reveals that partial time delays significantly affect phase synchronization in this system. In particular, partial time delays can

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... her enhance or decrease phase synchronization and induce synchronization transitions with changes in the mean firing rate of neurons, as well as induce switching between synchronized neurons with period-1 firing to synchronized neurons with period-2 firing. Moreover, in comparison to a neuronal network where all connections are delayed, we show that small partial time delay probabilities have especially different influences on phase synchronization of neuronal networks. Published by AIP Publishing. [http://dx.