Nonstationary transition to phase synchronization of neural networks induced by the coupling architecture

The transition to phase synchronized states of neural networks with bursting dynamics may have nonstationary characteristics, as well as sensitivity to initial conditions. Here, we analyze the paradigmatic network composed of neurons of Rulkov to investigate dynamic properties of the transitions to phase synchronization displayed by networks under two different topologies of the connection matrices, namely, small-world and random ones. Our analyses of both connection architectures reveal that neural networks under small-world topology display higher sensibility to initial conditions, and contrarily to the random connection case, depict a nonstationary transition to phase synchronization through the presence of a two-state on-off intermittency. The analyses are based on the recurrence quantifier determinism calculated by using only the local (mean) field potential (LFP) of the network, an experimentally easy accessible data. The use of LFP data offers advantages in the quantification of the nonstationary dynamics at the transition to phase synchronized states, since the more traditional Kuramoto order parameter must be computed over the individual signals of the neurons.