Title: Dynamics on (small) networks
Dynamical processes on networks include models of epidemic spreading, opinion formation and meme propagation. Often these models are formulated in terms of discrete time rules where a node updates its state on the basis of the states of its neighbours. While such models are often Markov chains, it is usually prohibitive to treat them as such because even a relatively small network can give rise to an extremely large state-space. In this talk, I’ll present a general model of dynamics on networks and illustrate what can be learnt from looking at cases that are sufficiently small to be treated exactly. As examples, I’ll discuss network versions of Schelling’s segregation model and Bonabeau’s model of hierarchy formation. I’ll also describe how network symmetries can be used to reduce the size of the state-space and various methods of approximating the dynamics.
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