Time-varying networks are prominently present in the nervous system, where the connections between neurons vary according to the activity of pre and post synapses. Using this as motivation, we here consider a system of two ephaptically coupled neurons with a periodically time-varying link between the two membrane potentials.

We derive the master stability function in dependence on the membrane potential coupling strength and in dependence on the ephaptic coupling strength. We first determine coupling ranges at which the two neurons are synchronizable if the link between them is static. In doing so, we find that the ephaptic coupling has a negligible impact on synchronization, while the coupling through the membrane potential has a strong effect.

We then consider switching in the coupling, determining the average synchronization error for a fixed ephaptic coupling strength and different membrane potential coupling strengths, and for various switching frequencies. We find the values of the switching coefficient that can synchronize the two neurons for each of the considered switching frequencies, and finally, we also use the basin stability method to determine the global stability of synchronization.

F. Parastesh, H. Azarnoush, M. Perc, et al., Synchronizability of two neurons with switching in the coupling, Applied Mathematics and Computation 350 (2019) 217–223