Coupled Networks, Patterns and Complexity - Abstract

McCullen, Nick

The serpentine route to patterns on networks.

Studies of Turing patterns in complex networks have revealed a rich set of behaviour [1]. Recent work at WIAS has made great progress explaining the origin of such behaviour [2]. Here we present the results of numerical investigations of the bifurcation structure involved in the transition from the initial Turing instability to the highly complex observed patterns. Particularly we observe behaviour related to homoclinic snaking seen for localised patterns in PDE systems [3]. newline References: newline [1] H. Nakao and A.S. Mikhailov, Nature Physics 6, 544--550 (2010). newline[2] M. Wolfrum, submitted to Physica D, WIAS-Preprint 1675 (2011). newline[3] Beck, M. et al., SIAM J. Math. Anal. 41, 3. 936--972 (2009).