2012/11/20 by Bob Rink, Rink, Bob, Jan A. Sanders +2 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Gene Regulatory Network Analysis #Nonlinear Dynamics and Pattern Formation #math.DS #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1211.4725
arxiv created 2012/11/20 · openalex publication_date 2012/11/20 · arxiv updated 2012/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous paper, the authors developed a method for computing normal forms of dynamical systems with a coupled cell network structure. We now apply this theory to one-parameter families of homogeneous feed-forward chains with 2-dimensional cells. Our main result is that Hopf bifurcations in such families generically generate branches of periodic solutions with amplitudes growing like λ1/2, λ1/6, λ1/18, etc. Such amplified Hopf branches were previously found by others in a subclass of feed-forward networks with three cells, first under a normal form assumption and later by explicit computations. We explain here how these bifurcations arise generically in a broader class of feed-forward chains of arbitrary length.