Global analysis of firing maps

Alexandre Mauroy, J.M. Hendrickx, Alexander Megretski, Rodolphe Sepulchre

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Résumé

— In this paper, we study the behavior of pulsecoupled integrate-and-fire oscillators. Each oscillator is characterized by a state evolving between two threshold values. As the state reaches the upper threshold, it is reset to the lower threshold and emits a pulse which increments by a constant value the state of every other oscillator. The behavior of the system is described by the so-called firing map: depending on the stability of the firing map, an important dichotomy characterizes the behavior of the oscillators (synchronization or clustering). The firing map is the composition of a linear map with a scalar nonlinearity. After briefly discussing the case of the scalar firing map (corresponding to two oscillators), the stability analysis is extended to the general n-dimensional firing map (for n + 1 oscillators). Different models are considered (leaky oscillators, quadratic oscillators,. . . ), with a particular emphasis on the persistence of the dichotomy in higher dimensions.
langue originaleAnglais
titreProceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS)
Pages1775-1782
Nombre de pages8
Etat de la publicationPublié - juil. 2010

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