Amplified steady state bifurcations in feedforward networks

TL;DR

This paper studies how the feedforward structure of coupled cell networks influences steady state bifurcations, revealing amplification effects and complex branching patterns depending on network parameters.

Contribution

It provides a new algorithm to analyze bifurcations in general feedforward networks using their structure, extending previous results on simpler chains.

Findings

Amplification of steady state growth rates due to feedforward structure

Different bifurcation patterns occur in various parameter regions

Algorithmic approach to determine bifurcations from network structure

Abstract

We investigate bifurcations in feedforward coupled cell networks. Feedforward structure (the absence of feedback) can be defined by a partial order on the cells. We use this property to study generic one-parameter steady state bifurcations for such networks. Branching solutions and their asymptotics are described in terms of Taylor coefficients of the internal dynamics. They can be determined via an algorithm that only exploits the network structure. Similar to previous results on feedforward chains, we observe amplifications of the growth rates of steady state branches induced by the feedforward structure. However, contrary to these earlier results, as the interaction scenarios can be more complicated in general feedforward networks, different branching patterns and different amplifications can occur for different regions in the space of Taylor coefficients.