### Abstract

Original language | English |
---|---|

Title of host publication | Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS) |

Pages | 1775-1782 |

Number of pages | 8 |

Publication status | Published - Jul 2010 |

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*Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS)*(pp. 1775-1782)

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*Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS).*pp. 1775-1782.

**Global analysis of firing maps.** / Mauroy, Alexandre; Hendrickx, J.M.; Megretski, Alexander; Sepulchre, Rodolphe.

Research output: Contribution in Book/Catalog/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Global analysis of firing maps

AU - Mauroy, Alexandre

AU - Hendrickx, J.M.

AU - Megretski, Alexander

AU - Sepulchre, Rodolphe

PY - 2010/7

Y1 - 2010/7

N2 - — 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.

AB - — 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.

M3 - Conference contribution

SP - 1775

EP - 1782

BT - Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS)

ER -