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arXiv · 1211.4725

Amplified Hopf bifurcations in feed-forward networks

Bob Rink·Jan Sanders
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Abstract

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 $λ^{1/2}$, $λ^{1/6}$, $λ^{1/18}$, 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.

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Bob Rink, Jan Sanders. 2012-11-20. Amplified Hopf bifurcations in feed-forward networks. https://arxiv.org/abs/1211.4725

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