Turing patterns on networks

Details Turing patterns on networks Turing patterns on networks

2008-07-08

arxiv.org/abs/0807.1230v1

Nature Physics (2010, completely revised and extended version)

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, 4 figures

Scientific paper

10.1038/nphys1651

Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical simulations, using a prey-predator model on a scale-free random network, demonstrate that the final, asymptotically reached Turing patterns can be largely different from the critical modes at the onset of instability, and multistability and hysteresis are typically observed. An approximate mean-field theory of nonlinear Turing patterns on the networks is constructed.

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