Amplified steady state bifurcations in feedforward networks. (7th April 2022)

• Record Type: Journal Article
• Authors: von der Gracht, Sören; Nijholt, Eddie; Rink, Bob
• Is Part Of: Nonlinearity. Volume 35:Number 4(2022)
• Page Start: 2073
• Page End: 2120
• Publication Date: 2022-04-07
• Subjects: steady state bifurcations -- network dynamics -- feedforward networks -- amplification; 37G10 -- 34D06; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac5463
• Languages: English
• ISSNs: 0951-7715

Abstract

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.