For a single neuron model, increased fluctuation in the spiking threshold results in increased variation in the inter spike interval. A multimodal ISI probability distribution is found.

Collective dynamics of the instantaneously coupled system exhibits strong to moderate synchrony with the increasing variance in the spiking threshold which could be revived by the effective gain of the coupling strength whereas for a constant variance of threshold, the computed synchronization parameter (χ²) is found to have a positive correlation with the coupling strength.

It is observed that increased fluctuation does not necessarily result in decrease in χ². Here, the synchronization is seen to be changing from complete to partial and vice-versa for certain range of the threshold parameter S. The Delay coupled neuronal model with constant coupling constant, appears to be in full synchrony for a very small range of values of spike threshold variation parameter. Moreover, this scenario is observed for a gradually decreasing time delay when the coupling connection between the neurons is more. For a constant time delay, strong to moderate synchrony is achieved by gradually increasing threshold variation.