TY - JOUR
T1 - Periodic solutions for an N-dimensional cyclic feedback system with delay
AU - Ivanov, Anatoli F.
AU - Lani-Wayda, Bernhard
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2020/4/15
Y1 - 2020/4/15
N2 - We study models for N cyclically coupled variables (e.g., neuron activities) with overall negative delayed feedback, and without symmetry or monotonicity properties. Our aim is to extract the common parts of similar approaches that are known in dimensions one, two and three so far, to exhibit how these parts work for general dimension N, and to show how this framework includes previous as well as new results. We provide a fixed point theorem and a related theorem on periodic orbits for semiflows on Banach spaces, which then yield periodic solutions of cyclic delayed negative feedback systems for general N. We also give criteria for the global asymptotic stability in the same systems, which are derived by relating the systems to interval maps.
AB - We study models for N cyclically coupled variables (e.g., neuron activities) with overall negative delayed feedback, and without symmetry or monotonicity properties. Our aim is to extract the common parts of similar approaches that are known in dimensions one, two and three so far, to exhibit how these parts work for general dimension N, and to show how this framework includes previous as well as new results. We provide a fixed point theorem and a related theorem on periodic orbits for semiflows on Banach spaces, which then yield periodic solutions of cyclic delayed negative feedback systems for general N. We also give criteria for the global asymptotic stability in the same systems, which are derived by relating the systems to interval maps.
UR - http://www.scopus.com/inward/record.url?scp=85075878898&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85075878898&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2019.11.028
DO - 10.1016/j.jde.2019.11.028
M3 - Article
AN - SCOPUS:85075878898
SN - 0022-0396
VL - 268
SP - 5366
EP - 5412
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 9
ER -