Global analysis of Firing Maps
(2010) Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS2010) — Location: Budapest, Hungary
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- Abstract
- 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
- Affiliations
Uliège Montefiore Massachusetts Institute of Technology LIDS
Citations
Mauroy, A., Hendrickx, J., Megretski, A., & Sepulchre, R. (2010). Global analysis of Firing Maps. Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS2010). Published. Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS2010), Budapest, Hungary. https://hdl.handle.net/2078.5/254733