January 24, 2012, HFH 4164

The study of networks of pulse-coupled firing oscillators is a general and simple paradigm to investigate a wealth of natural phenomena (brain neurons, earthquakes, animal behaviors, etc.). In this framework, the oscillators of the network interact through an instantaneous impulsive coupling: whenever an oscillator fires, it sends out a pulse which instantaneously increments the state of the other oscillators by a constant value. It is a remarkable fact that networks of pulse-coupled oscillators usually exhibit a dichotomic behavior: either the oscillators achieve perfect synchrony or they converge toward an anti-synchronized configuration. Interestingly, theoretical results confirm the dichotomic behavior for a large class of oscillators, but also suggest that the dichotomic behavior is not a general feature of every network of pulse-coupled oscillators. In this talk, I will present stability results both for finite and infinite populations of pulse-coupled oscillators as well as several related open problems.

Alexandre Mauroy received the Ph.D. degree in 2011 from the University of Liège (ULg), Belgium (under supervision of Rodolphe Sepulchre) and graduated in 2007 in Aerospace Engineering from ULg. From October 2007 to October 2011, he worked in the Department of Electrical Engineering and Computer Science at ULg as a FNRS research fellow. He is currently working in the Department of Mechanical Engineering at UCSB as a BAEF postdoctoral researcher (host professor: Igor Mezic). His main interests focus on the dynamics of coupled oscillators and on the collective behaviors in large networks (e.g. synchronization).