ORBi: Mauroy Alexandre - Global Analysis of Firing Maps

Reference : Global Analysis of Firing Maps


	Document type :	Scientific congresses and symposiums : Paper published in a book
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics Engineering, computing & technology : Multidisciplinary, general & others
	To cite this reference:	http://hdl.handle.net/2268/69740

Title :	Global Analysis of Firing Maps
Language :	English
Author, co-author :	Mauroy, Alexandre [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 [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Publication date :	Jul-2010
Main document title :	Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems
Pages :	1775-1782
On invitation :	No
Audience :	International
Event name :	19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010)
Event date :	5-9 july 2010
Event place (city) :	Budapest
Event country :	Hungary
Keywords :	[en] stability ; discrete map ; pulse-coupled oscillators
Abstract :	[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.
Funders :	Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS
Target :	Researchers ; Professionals
Permalink :	http://hdl.handle.net/2268/69740
Other URL :	http://www.montefiore.ulg.ac.be/~mauroy/MTNS2010_MHMS.pdf

File(s) associated to this reference

Fulltext file(s):

	File	Commentary	Version	Size	Access
Open access	313_360.pdf		Publisher postprint	246.77 kB	View/Open
Open access	MTNS2010MHMSreport.pdf	technical note: proof of Proposition 4	Publisher postprint	95.12 kB	View/Open

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