WIAS Preprint No. 1675, (2012)

The Turing bifurcation in network systems: Collective patterns and single differentiated nodes



Authors

  • Wolfrum, Matthias

2008 Physics and Astronomy Classification Scheme

  • 89.75Fb 89.75Kd

Keywords

  • Turing instability, Diffusively coupled networks, Localized patterns

Abstract

We study the emergence of patterns in a diffusively coupled network that undergoes a Turing instability. Our main focus is the emergence of stable solutions with a single differentiated node in systems with large and possibly irregular network topology. Based on a mean-field approach, we study the bifurcations of such solutions for varying system parameters and varying degree of the differentiated node. Such solutions appear typically before the onset of Turing instability and provide the basis for the complex scenario of multistability and hysteresis that can be observed in such systems. Moreover, we discuss the appearance of stable collective patterns and present a codimension-two bifurcation that organizes the interplay between collective patterns and patterns with single differentiated nodes.

Appeared in

  • Phys. D, 241 (2012) pp. 1351--1357.

Download Documents