title: Renewal Approach to the Analysis of the Asynchronous State for Coupled Noisy Oscillators.
abstract: We develop a framework in which the activity of nonlinear pulse-coupled oscillators is posed within the renewal theory. In this approach, the evolution of the interevent density allows for a self-consistent calculation that determines the asynchronous state and its stability. This framework can readily be extended to the analysis of systems with more state variables and provides a population density treatment to evolve them in their thermodynamical limits. To demonstrate this we study a nonlinear pulse-coupled system, where couplings are dynamic and activity dependent. We investigate its stability and numerically study the nonequilibrium behavior of the system after the bifurcation. We show that this system undergoes a supercritical Hopf bifurcation to collective synchronization.
authors.affiliation: Neuroinformatics & Theoretical Neuroscience, Freie Universität Berlin and BCCN-Berlin, 14195 Berlin, Germany.
authors.forename: Farzad
authors.initials: F
authors.lastname: Farkhooi
authors.affiliation: Centre de Neurophysique Physiologie et Pathologie, Université Paris Descartes and CNRS UMR 8119, 75270 Paris Cedex 06, France.
authors.forename: Carl
authors.initials: C
authors.lastname: van Vreeswijk
mesh_terms: D001683:Biological Clocks; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D013816:Thermodynamics