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.
| Original language | English |
|---|---|
| Article number | 76 |
| Pages (from-to) | 1-15 |
| Number of pages | 15 |
| Journal | Electronic Journal of Qualitative Theory of Differential Equations |
| Volume | 2020 |
| DOIs | |
| Publication status | Published - 21 Dec 2020 |
Bibliographical note
Funding Information:D. Franco and J. Perán were supported by grant MTM2017-85054-C2-2-P (AEI/FEDER, UE) and ETSII-UNED grant 2020-MAT10. D. Franco was supported by grant PRX19/00582 of the Ministerio de Educación, Cultura y Deporte (Subprograma Estatal de Movilidad). D. Franco thanks the Department of Mathematical Sciences of the University of Bath (UK) for its generous hospitality during a sabbatical leave.
Publisher Copyright:
© 2020, University of Szeged. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
Funding
D. Franco and J. Perán were supported by grant MTM2017-85054-C2-2-P (AEI/FEDER, UE) and ETSII-UNED grant 2020-MAT10. D. Franco was supported by grant PRX19/00582 of the Ministerio de Educación, Cultura y Deporte (Subprograma Estatal de Movilidad). D. Franco thanks the Department of Mathematical Sciences of the University of Bath (UK) for its generous hospitality during a sabbatical leave.
Keywords
- Delay differential equations
- Difference equations
- Global attractor
ASJC Scopus subject areas
- Applied Mathematics