# Pattern Formation in Random Networks Using Graphons

@inproceedings{Bramburger2021PatternFI, title={Pattern Formation in Random Networks Using Graphons}, author={Jason J. Bramburger and Matt Holzer}, year={2021} }

We study Turing bifurcations on one-dimensional random ring networks where the probability of a connection between two nodes depends on the distance between the two nodes. Our approach uses the theory of graphons to approximate the graph Laplacian in the limit as the number of nodes tends to infinity by a nonlocal operator – the graphon Laplacian. For the ring networks considered here, we employ center manifold theory to characterize Turing bifurcations in the continuum limit in a manner…

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