abstr20
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.