Robustness of Diversity Induced Synchronization Transition in a Delayed Small-World Neuronal Network

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).