Comparison of solutions for non-monotone dynamical systems

Comparison of solutions for non-monotone dynamical systems

We give conditions for a non-monotone system to preserve the usual vector order of solutions for a subset of initial conditions. Our approach consists of separating terms that meet Kamke’s sign condition from other ones in the dynamics, and considering Picard iterations. These conditions amount for...

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Veröffentlicht in:Systems & control letters 2024-09, Vol.191 (105862), p.105862, Article 105862
Hauptverfasser: Rapaport, Alain, Laraj, Oumaima, Khattabi, Noha El
Format: Artikel
Sprache:eng
Schlagworte:
Dynamical Systems
Mathematics
Monotone systems
Ordinary differential equations
Partial order
Solutions comparison
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Zusammenfassung:We give conditions for a non-monotone system to preserve the usual vector order of solutions for a subset of initial conditions. Our approach consists of separating terms that meet Kamke’s sign condition from other ones in the dynamics, and considering Picard iterations. These conditions amount for the dynamics to preserve a partial order, which is not necessarily induced by a cone. Examples illustrate the results.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2024.105862