The Mathematics Department presents Dr. Sebastian van Strienonn “Dynamics of expanding maps in heterogeneous networks” on Monday, May 12, at 4 p.m. in Morton 326.
Sebastian Van Strien
Strien is with the Department of Mathematics at Imperial College in London.
Abstract: We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic approach which enables us to describe the effective dynamics of the massively connected nodes when taking a weak interaction limit. More precisely, we show that for almost every random network and almost all initial conditions the high dimensional network governing the dynamics of the massively connected nodes can be reduced to a few macroscopic equations. Such reduction is intimately related to the ergodic properties of the expanding maps. This reduction allows one to explore the coherent properties of the network.
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