Evaluating the robustness of activator-inhibitor models for cluster head computation

Abstract

Activator-inhibitor models have been widely used to explain several morphogenetic processes. They have also been used to engineer algorithms for computer graphics, distributed systems and networks. These models are known to be robust to perturbations such as the removal of peaks of chemicals. However little has been reported about their actual quantitative performance under such disruptions. In this paper we experimentally evaluate the robustness of two well-known activator-inhibitor models in the presence of attacks that remove existing activator peaks. We focus on spot patterns used as distributed models for cluster head computation, and on their potential implementation in chemical computing. For this purpose we derive the corresponding chemical reactions, and simulate the system deterministically. Our results show that there is a trade-off between both models. The chemical form of the first one, the Gierer-Meinhardt model, is slow to recover due to the depletion of a required catalyst. The second one, the Activator-Substrate model, recovers more quickly but is also more dynamic as peaks may slowly move. We discuss the implications of these findings when engineering algorithms based on morphogenetic models. © 2010 Springer-Verlag Berlin Heidelberg.