On the global attractor of delay differential equations with unimodal feedback not satisfying the negative Schwarzian derivative condition

Franco, Daniel; Guiver, Chris; Logemann, Hartmut; Per�n, Juan

Abstract

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

• Journal Article Type: Article
• Acceptance Date: Sep 11, 2020
• Online Publication Date: Dec 21, 2020
• Publication Date: 2020
• Deposit Date: Dec 11, 2020
• Publicly Available Date: Dec 21, 2020
• Journal: Electronic Journal of Qualitative Theory of Differential Equations
• Peer Reviewed: Peer Reviewed
• Issue: 76
• Pages: 1-15
• DOI: https://doi.org/10.14232/ejqtde.2020.1.76
• Keywords: Delay differential equations, difference equations, global attractor
• Public URL: http://researchrepository.napier.ac.uk/Output/2710451