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Juan G. Restrepo, Postdoc with Alain Karma at the Center for Interdisciplinary Research on Complex Systems, Northeastern聽University

Dynamics on complex networks: synchronization, percolation, and the dynamical importance of nodes and links.

There has been much recent interest in studying dynamical processes on networks due to the realization that they provide a framework to understand mayn real world phenomena, and that many of these networks arising in applications share common structural properties. I will review recent progress on network dynamics, focusing on the emergence of synchronization in ensembles of coupled dynamical systems. Our main result is that the largest eigenvalue of the adjacency matrix of the coupling network, lambda, determines the critical coupling strength for the onset of synchronization. Similarly, lambda determines in some cases the fraction of nodes that need to be removed from a network in order to break it apart. Based on these results, we propose a characterization of the dynamical importance of nodes in terms of their contribution to lambda. I will discuss some implications of this characterization in the context of real-world examples. Finally, I will briefly discuss current work in intracellular calcium dynamics, where synchronization of calcium release from discrete sites in cardiac cells might play a role in promoting a life-threatening period doubling bifurcation.