Transversality for Cyclic Negative Feedback Systems
Dynamical Systems
2016-10-31 v1
Abstract
Transversality of stable and unstable manifolds of hyperbolic periodic trajectories is proved for monotone cyclic systems with negative feedback. Such systems in general are not in the category of monotone dynamical systems in the sense of Hirsch. Our main tool utilized in the proofs is the so-called cone of high rank. We further show that stable and unstable manifolds between a hyperbolic equilibrium and a hyperbolic periodic trajectory, or between two hyperbolic equilibria with different dimensional unstable manifolds also intersect transversely.
Cite
@article{arxiv.1412.1540,
title = {Transversality for Cyclic Negative Feedback Systems},
author = {Yi Wang and Dun Zhou},
journal= {arXiv preprint arXiv:1412.1540},
year = {2016}
}