On the global attractor of delay differential equationswith unimodal feedback not satisfying the negativeSchwarzian derivative condition

摘要

We study the size of the global attractor for a delay differential equation withunimodal feedback. We are interested in extending and complementing a dichotomyresult by Liz and R?st, which assumed that the Schwarzian derivative of the nonlinearfeedback is negative in a certain interval. Using recent stability results for differenceequations, we obtain a stability dichotomy for the original delay differential equationin the situation wherein the Schwarzian derivative of the nonlinear term may changesign. We illustrate the applicability of our results with several examples..