Title :
Local stability results for the collective behaviors of infinite populations of pulse-coupled oscillators
Author :
Mauroy, Alexandre ; Sepulchre, Rodolphe
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Univ. of Liege, Liege, Belgium
Abstract :
In this paper, we investigate the behavior of pulse-coupled integrate-and-fire oscillators. Because the stability analysis of finite populations is intricate, we investigate stability results in the approximation of infinite populations. In addition to recovering known stability results of finite populations, we also obtain new stability results for infinite populations. In particular, under a weak coupling assumption, we solve for the continuum model a conjecture still prevailing in the finite dimensional case.
Keywords :
multidimensional systems; oscillators; stability; collective behaviors; continuum model; finite dimensional case; infinite population; local stability; pulse-coupled integrate-and-fire oscillator; stability analysis; weak coupling assumption; Analytical models; Couplings; Eigenvalues and eigenfunctions; Equations; Mathematical model; Oscillators; Stability analysis;
Conference_Titel :
Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
978-1-61284-800-6
Electronic_ISBN :
0743-1546
DOI :
10.1109/CDC.2011.6160621
