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Imperial College London, UK <\/p>\n\n\n\n
Title:<\/strong> Mean-field and fluctuations for hub dynamics in heterogeneous random networks<\/p>\n\n\n\n Abstract:<\/strong> We consider heterogeneous random networks, where the network degree distribution follows a power-law, and each node dynamics is a random dynamical system, interacting with neighboring nodes via a random coupling function. We characterize the hub behavior by the mean-field, subject to statistically controlled fluctuations. In particular, we prove that the fluctuations are small over exponentially long time scales. Our results provide an explanation for several numerical observations, namely, a scaling relation between system size and frequency of large fluctuations, system size induced desynchronization, and Gaussian behavior of the fluctuations. This is joint work with Zheng Bian (Clarkson\/UNSW) and Tiago Pereira (USP).<\/p>\n\n\n\n Bio:<\/strong> Jeroen S.W. Lamb is a Professor of Mathematics at Imperial College London. His main current interest concerns the dynamics and bifurcations of random dynamical systems. He was a postdoc with Ian Stewart (1995-1997) and Martin Golubitsky (1998), before taking up his position at Imperial College in 1999.<\/p>\n\n\n\n