Protocol for suppression of phase synchronization in Hodgkin–Huxley-type networks

Phase synchronization of neurons is fundamental for the functioning of the human brain which can be related to neurological diseases such as Parkinson and/or seizure behaviors generated by epilepsy. For small-world networks, an atypically high level of phase synchronization may occur even for unexpected low values of the coupling strength when compared to traditional critical values which delimit the transition from a globally stable unsynchronized to a globally stable phase synchronized states. This regime is characterized by a non-monotonic transition as a function of the coupling parameter. In order to study this phenomenon, we consider a neural network composed of 5,000 Hodgkin–Huxley-type neurons, coupled by a small-world connection matrix. Based on suppression protocols of phase synchronization, we study how this abnormal phase synchronization can be suppressed by applying an external pulsed current in the network. It is shown that the synchronization for weak coupling can be suppressed without any visible effect in the globally stable asymptotic state occurring for higher values of the coupling strength. We also demonstrate that to preserve the unsynchronized state, the external current must be kept switched on, otherwise, the abnormal synchronization regime is recovered due to the globally stable state present on the dynamics. Optimization protocols are studied by varying the amplitude and time intervals of the current pulses.