The role of local dynamics in the phase synchronization process of a network

Partial phase synchronization, also reported as neuron cooperation, is a pivotal behavior of the brain and related to its main features, such as memory. The excess or even the lack of phase synchronization are associated with brain disorders like epilepsy and Parkinson's disease. These diseases may be related to malfunctioning of the synchronization process of the neurons, triggered by changes of the local dynamics of the neurons influenced by parameters such as the ion-channel conductance. In fact, it is common the use of drugs to block or activate specific channels, changing the conductance and bringing the synchronization process to some desired behavior. We report here how individual characteristics of the local dynamics of the neurons, such as their linear stability, when coupled in a network may be a fundamental

player in the phase synchronization process as a function of the coupling strength. Global and small-world topologies are considered. For both coupling schemes, the effects of the local dynamics are clear, inducing early or retarding the occurrence of partial phase synchronization of the network when the coupling strength is varied. In this scenario, we discuss the effect of the local dynamics of the neuron, showing it may be of fundamental importance to understand and control the process of the network phase synchronization. The study also brings useful information to the general understanding of network-phase-synchronization processes.