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SYBN: Biological and Social Networks

SYBN 3: Biologische und Soziale Netzwerke, Postersitzung

SYBN 3.33: Poster

Montag, 7. März 2005, 14:00–15:30, Poster TU E

Dynamic hierarchy in a network of chaotic maps with distributed sizes: application to epidemic outbreaks in city-networks — •Bernd Blasius — Institut f. Physik, Nichtlineare Dynamik, Universitaet Potsdam

We develop a theory for the dynamics of recurrent epidemic outbreaks and their synchronization in a network of coupled cities. The dynamics in each city is described by a one-dimensional map, which generates chaotic outbreak dynamics in excellent agreement with long-term data sets. To study the synchronization in a network of interacting cities we assume that the coupling topology is fully determined by the city-size distribution. In particular, we focus on the case where the interaction between two nodes depends on their size ratio. This gives rise to a network with dominance topology, where large nodes are able to influence smaller ones. To describe the network we calculate the degree distribution and clustering coefficient. In the coupled network we observe a dynamic hierarchy, i.e. by increasing a node’s rank the dynamics follows a period doubling bifurcation. Thus, the mean field can show regular oscillations even though the uncoupled maps are in the range of fully developed chaos. Similar regular oscillations of the synchronization index are observed in real data.