Projection blocks in homogeneous coupled cell networks

TL;DR

This paper introduces projection blocks in homogeneous coupled cell networks, providing a method to analyze bifurcations by simplifying the network structure, and applies this to generalized feed-forward networks with complex loops.

Contribution

It defines projection blocks and demonstrates their use in understanding bifurcations in complex coupled cell networks, extending previous methods.

Findings

Projection blocks help analyze bifurcations in complex networks

Identifying projection blocks simplifies the network analysis

Application to generalized feed-forward networks with multiple cells in loops

Abstract

We introduce a special subset of the graph of a homogeneous coupled cell network, called a projection block, and show that the network obtained from identifying this block to a single point can be used to understand the generic bifurcations of the original network. This technique is then used to describe the bifurcations in a generalized feed-forward network, in which the loop can contain more than one cell.