title: Synergistic effect of repulsive inhibition in synchronization of excitatory networks.
abstract: We show that the addition of pairwise repulsive inhibition to excitatory networks of bursting neurons induces synchrony, in contrast to one's expectations. Through stability analysis, we reveal the mechanism underlying this purely synergistic phenomenon and demonstrate that it originates from the transition between different types of bursting, caused by excitatory-inhibitory synaptic coupling. This effect is generic and observed in different models of bursting neurons and fast synaptic interactions. We also find a universal scaling law for the synchronization stability condition for large networks in terms of the number of excitatory and inhibitory inputs each neuron receives, regardless of the network size and topology. This general law is in sharp contrast with linearly coupled networks with positive (attractive) and negative (repulsive) coupling where the placement and structure of negative connections heavily affect synchronization.
authors.affiliation: Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, Georgia 30303, USA.
authors.forename: Igor
authors.initials: I
authors.lastname: Belykh
authors.affiliation: Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, Georgia 30303, USA.
authors.forename: Reimbay
authors.initials: R
authors.lastname: Reimbayev
authors.affiliation: Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, Georgia 30303, USA.
authors.forename: Kun
authors.initials: K
authors.lastname: Zhao
mesh_terms: D008959:Models, Neurological; D009415:Nerve Net / Q000166:cytology* / Q000502:physiology*; D009433:Neural Inhibition; D009474:Neurons / Q000166:cytology; D013569:Synapses / Q000502:physiology