The strong unstable manifold and periodic solutions in differential delay equations with cyclic monotone negative feedbck
| Autor: | Lani-Wayda, Bernhard, Ivanov, Anatoli F. |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For a class of $(N+1)$-dimensional systems of differential delay equations with a cyclic and monotone negative feedback structure, we construct a two-dimensional invariant manifold, on which phase curves spiral outward towards a bounding periodic orbit. For this to happen we assume essentially only instability of the zero equilibrium. Methods of the Poincar\'e-Bendixson theory due to Mallet-Paret and Sell are combined with techniques used by Walther for the scalar case $(N = 0)$. Statements on the attractor location and on parameter borders concerning stability and oscillation are included. The results apply to models for gene regulatory systems, e.g. the `repressilator' system. Comment: 34 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|