Seminar Details
2011-11-08 (14.00) : Dichotomic collective behaviors in networks of pulse-coupled oscillators
At Euler building
Organized by Mathematical Engineering
Speaker :
Mauroy, Alexandre
Abstract :
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.