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Lectures on Complex Networks$
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Sergey Dorogovtsev

Print publication date: 2010

Print ISBN-13: 9780199548927

Published to Oxford Scholarship Online: May 2010

DOI: 10.1093/acprof:oso/9780199548927.001.0001

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Interacting systems on networks

Interacting systems on networks

(p.99) 13 Interacting systems on networks
Lectures on Complex Networks

Sergey N. Dorogovtsev

Oxford University Press

This chapter considers systems of interacting agents placed on networks. The agents — spins, oscillators, interacting individuals, etc. — occupy the nodes of networks and interact with each other through network links. In more complicated situations, these agents, in turn, influence their network substrates, and so the pair, a network and the system of agents, co-evolve. The chapter discusses unusual phenomena in these cooperative systems on complex networks. In particular, the Ising model on networks is considered, various synchronization phenomena, and basic game theory models. Finally, avalanches and other abrupt phenomena in many-particle systems on complex networks are touched upon.

Keywords:   Ising model, critical temperature, synchronization, synchronizability, prisoner's dilemma, avalanches

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