DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Paul So, George Mason University

**Title: ***
The emergence of macroscopic chaos and crisis in a network of globally coupled phase oscillators
*

**Abstract:**
The Kuramoto system has been a very successful model in demonstrating the emergence of collective rhythm from coupled biological and physical networks ranging from populations of fireflies, coupled neurons in the brain, to Josephson Junction arrays. A recent remarkable result from [Ott & Antonsen, Chaos 18, 037113 (2008)] has provided an analytical tool to reduce the infinite dimensional system to a low dimensional set of ODEs for the macroscopic meanfield. This result was recently extended to the dynamical analysis of networks consisting of distinct subnetworks and networks with time varying coupling. These extensions were motivated by real neurological networks in which there are interacting subpopulations of neurons and intrinsic time variations. From the current work on this system, we were able to show that the macroscopic meanfield can behave chaotically. Cascades of periodic doubling bifurcations and crises were identified. This is the first demonstration that macroscopic chaos is possible for a network of globally coupled phase oscillators.

**Time:** Friday, October 8, 2010, 1:30-2:30 p.m.

**Place:** Science and Tech I, Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491