(Electronic Journal of Qualitative Theory of Differential Equations, 2020-12-21) Franco Leis, Daniel; Guiver, Chris; Logemann, Harmut; Perán Mazón, Juan Jacobo; Kriszrin, Tibor; Webb, Jeff R. L.
We study the size of the global attractor for a delay differential equation with unimodal feedback. We are interested in extending and complementing a dichotomy result by Liz and Röst, which assumed that the Schwarzian derivative of the nonlinear feedback is negative in a certain interval. Using recent stability results for difference equations, we obtain a stability dichotomy for the original delay differential equation in the situation wherein the Schwarzian derivative of the nonlinear term may change sign. We illustrate the applicability of our results with several examples.
