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.
| Original language | English |
|---|---|
| Pages (from-to) | 2073-2120 |
| Number of pages | 48 |
| Journal | Nonlinearity |
| Volume | 35 |
| Issue number | 4 |
| Early online date | 7 Mar 2022 |
| DOIs | |
| Publication status | Published - Apr 2022 |
Bibliographical note
Funding Information:This research is partly financed by the Dutch Research Council (NWO) via Eddie Nijholt’s research program ‘Designing Network Dynamical Systems through Algebra’.
Funding Information:
Bob Rink is happy to acknowledge the hospitality and financial support of the Sydney Mathematical Research Institute.
Publisher Copyright:
© 2022 IOP Publishing Ltd & London Mathematical Society.
Funding
This research is partly financed by the Dutch Research Council (NWO) via Eddie Nijholt’s research program ‘Designing Network Dynamical Systems through Algebra’. Bob Rink is happy to acknowledge the hospitality and financial support of the Sydney Mathematical Research Institute.
Keywords
- amplification
- feedforward networks
- network dynamics
- steady state bifurcations