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This paper presents an in-reachability based classification of invariantsynchrony patterns in Coupled Cell Networks (CCNs). These patterns are encodedthrough partitions on the set of cells, whose subsets of synchronized cells arecalled colors. We study the influence of the structure of the network in thequalitative behavior of invariant synchrony sets, in particular, with respectto the different types of (cumulative) in-neighborhoods and the in-reachabilitysets. This motivates the proposed approach to classify the partitions into thecategories of strong, rooted and weak, according to how their colors arerelated with respect to the connectivity structure of the network. Furthermore,we show how this classification system acts under the partition join ($ \vee $)operation, which gives us the synchrony pattern that corresponds to theintersection of synchrony sets.

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