In a diverse and delayed small-world neuronal network,we have identified the oscillatory-like synchronization transition between anti-phase and complete synchronization[Phys.Rev.E 83(2011)046207].Here we study the influence of the network topology and noise on the synchronization transition.The robustness of this transition is investigated.The results show that:(i)the synchronization transition is robust to the neuron number N in the network;(ii)only when the coupled neighbor number k is in the region[4,10],does the synchronization transition exist;(iii)to some extent,the synchronization is destroyed by noise and the oscillatory−like synchronization transition exists for relatively weak noise(D<0.003).
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