title: Modeling the network dynamics of pulse-coupled neurons.
abstract: We derive a mean-field approximation for the macroscopic dynamics of large networks of pulse-coupled theta neurons in order to study the effects of different network degree distributions and degree correlations (assortativity). Using the ansatz of Ott and Antonsen [Chaos 18, 037113 (2008)], we obtain a reduced system of ordinary differential equations describing the mean-field dynamics, with significantly lower dimensionality compared with the complete set of dynamical equations for the system. We find that, for sufficiently large networks and degrees, the dynamical behavior of the reduced system agrees well with that of the full network. This dimensional reduction allows for an efficient characterization of system phase transitions and attractors. For networks with tightly peaked degree distributions, the macroscopic behavior closely resembles that of fully connected networks previously studied by others. In contrast, networks with highly skewed degree distributions exhibit different macroscopic dynamics due to the emergence of degree dependent behavior of different oscillators. For nonassortative networks (i.e., networks without degree correlations), we observe the presence of a synchronously firing phase that can be suppressed by the presence of either assortativity or disassortativity in the network. We show that the results derived here can be used to analyze the effects of network topology on macroscopic behavior in neuronal networks in a computationally efficient fashion.
authors.affiliation: University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Sarthak
authors.identifier: 0000000230478334
authors.initials: S
authors.lastname: Chandra
authors.affiliation: Case Western Reserve University, Cleveland, Ohio 44016, USA.
authors.forename: David
authors.initials: D
authors.lastname: Hathcock
authors.affiliation: Iowa State University, Ames, Iowa 50011, USA.
authors.forename: Kimberly
authors.initials: K
authors.lastname: Crain
authors.affiliation: University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Thomas M
authors.initials: TM
authors.lastname: Antonsen
authors.affiliation: University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Michelle
authors.initials: M
authors.lastname: Girvan
authors.affiliation: University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Edward
authors.initials: E
authors.lastname: Ott
mesh_terms: D003198:Computer Simulation; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D009716:Numerical Analysis, Computer-Assisted