Reference : Global Analysis of Firing Maps
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http://hdl.handle.net/2268/69740
Global Analysis of Firing Maps
English
Mauroy, Alexandre mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Hendrickx, Julien [Massachusetts Institute of Technology - MIT > Electrical Engineering and Computer Science > Laboratory for Information and Decision Systems > >]
Megretski, Alexandre [Massachusetts Institute of Technology - MIT > Electrical Engineering and Computer Science > Laboratory for Information and Decision Systems > >]
Sepulchre, Rodolphe mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Jul-2010
Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems
1775-1782
Yes
No
International
19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010)
5-9 july 2010
Budapest
Hungary
[en] stability ; discrete map ; pulse-coupled oscillators
[en] In this paper, we study the behavior of pulse-coupled 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.
Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS
Researchers ; Professionals
http://hdl.handle.net/2268/69740
http://www.montefiore.ulg.ac.be/~mauroy/MTNS2010_MHMS.pdf

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