Existence and Partial Characterization of the Global Attractor for the Sunflower Equation

This paper is devoted to the study of some global dynamical properties of the so-called sunflower equation ϵx′′(t) + ax′(t) + b sin x(t − ϵ) = 0, ϵ > 0. It is shown that considering this equation as retarded differential equation on S1 ± R, it has a global attractor for any ϵ > 0, which is homeomorphic to S1 for any ϵ ∈ [0, a/b