Impact of random links on neuronal extreme events

We explore the influence of random connections on the creation of extreme events in the spiking patterns of the action potentials of model neurons diffusively coupled in networks. We find that the presence of a small fraction p of static random links in the network suppresses extreme events, while a high fraction of such links induce extreme events for sufficiently high coupling strengths. Interestingly, when the random links are time-varying, even a small number of such links can make the network prone to extreme events in a significant range of coupling strength. We also find the phenomena of synchronized extreme events emerging in the network under random connections, and these events are more catastrophic in nature as they occur concurrently across the network. Additionally, when the random links are dynamically switched, even a very small fraction of random links in the system leads to such synchronous extreme spiking events. We also explore the dependence of the probability of extreme events PXE on the frequency f of rewiring. The only significant change in PXE under variation of f is observed for intermediate values of p, where we obtain a sharp transition to a regime with high PXE after a critical rewiring frequency fc. Importantly, the value of fc is very small for strong coupling, implying that even slowly varying networks yield significantly higher number of extreme events than static networks. Lastly, we find that the variability of PXE becomes large when the network is on the verge of a transition to a regime where the probability of extreme events is significantly high. So this feature can be utilized as an early warning signal, and has potential implications for extreme-event risk appraisal in dynamical networks.