title: Eckhaus instability in systems with large delay.
abstract: The dynamical behavior of various physical and biological systems under the influence of delayed feedback or coupling can be modeled by including terms with delayed arguments in the equations of motion. In particular, the case of long delay may lead to complicated and high-dimensional dynamics. We investigate the effects of delay in systems that display an oscillatory instability (Hopf bifurcation) in the absence of delay. We show by analytical and numerical methods that the dynamical scenario includes the coexistence of multiple stable periodic solutions and can be described in terms of the Eckhaus instability, which is well known in the context of spatially extended systems.
authors.affiliation: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany. wolfrum@wias-berlin.de
authors.forename: Matthias
authors.initials: M
authors.lastname: Wolfrum
authors.forename: Serhiy
authors.initials: S
authors.lastname: Yanchuk
mesh_terms: D001683:Biological Clocks; D005246:Feedback; D008432:Mathematical Computing; D008954:Models, Biological; D008962:Models, Theoretical