Unraveling the dynamics of a flux coupled Chialvo neurons and the existence of extreme events.

To illustrate the occurrences of extreme events in the neural system we consider a pair of Chialvo neuron maps. Importantly, we explore the dynamics of the proposed system by including a flux term between the neurons. Primarily, the dynamical behaviors of the coupled Chialvo neurons are examined using the Lyapunov spectrum and bifurcation analysis. We find the transitions between the periodic and chaotic dynamics in relation to the injected ion current of the first and second neurons and the flux coupling strength. It is interesting to note that, the extreme events can occur in the chaotic zone for some parameters. The analysis is then extended to a network of Chialvo neurons with various network connectivities. We discover that coexisting coherent and incoherent behaviour can arise and that nodes in the network can exhibit extreme event features. The findings of this study could help to better understand the rare large-amplitude events that occur in neural networks, which can help detect and prevent a variety of neurological disorders.