An in-reachability based classification of invariant synchrony patterns in weighted coupled cell networks

Abstract

Abstract This paper presents an in-reachability based classification of invariant synchrony patterns in coupled cell networks (CCNs). These patterns are encoded through partitions on the set of cells, whose subsets of synchronised cells are called colours. We study the influence of the structure of the network in the qualitative behaviour of invariant synchrony sets, in particular, with respect to the different types of (cumulative) in-neighbourhoods and the in-reachability sets. This motivates the proposed approach to classify the partitions into the categories of strong, rooted and weak, according to how their colours are related with respect to the connectivity structure of the network. Furthermore, we show how this classification system acts under the partition join ( ∨ ) operation, which gives us the synchrony pattern that corresponds to the intersection of synchrony sets.