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Regulating the coupling strength of neurons by noise, we numerically study the effect of the fluctuation of coupling strength on the synchronization of scale-free neuronal network with time delays. It is found that the neurons exhibit synchronization transitions when noise intensity is varied, and the synchronization transitions are delay-dependent and are enhanced at certain time delays. This phenomenon becomes stronger for chemical coupling than for electrical coupling. As network average degree increases, this phenomenon decreases monotonically for electrical coupling. However, for chemical coupling there is an optimal network average degree at which the phenomenon becomes strongest. These results show that the fluctuation of coupling strength can induce different synchronization transitions in scale-free neuronal network. This implies that random coupling strength could play a crucial role in the information transmission in neural systems.
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