SELF-INDUCED SYNCHRONIZATION BY LARGE DELAY - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

SELF-INDUCED SYNCHRONIZATION BY LARGE DELAY

Résumé

We investigate the dynamics of a delay differential equation obtained by perturbing a vector field f : R n → R n , admitting a stable periodic orbit, thanks to a delayed feedback control ηg(x, x(t − τ)) of same regularity, where η is small and τ large so that ητ be bounded but non small. We prove that trajectories starting in a neighborhood (of size independent on the parameters η, τ) of this original periodic orbit in the set of continuous functions from [−τ, 0] to R n enter asymptotically a periodic regime, which regimes existing in finite number. Our synchronization result is based on the construction of an invariant manifold via a process inspired by the Lyapunov-Perron method for integral operators associated to solutions of ordinary differential equations, and on the persistence of normally hyperbolic invariant manifolds for semi-flows on Banach spaces. The statement we provide here complements already known results on periodic orbits in the context of delay differential equations.
Fichier principal
Vignette du fichier
SelfSync-FEBRUARY-24-2021.pdf (513.56 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03183760 , version 1 (28-03-2021)

Identifiants

  • HAL Id : hal-03183760 , version 1

Citer

Camille Poignard. SELF-INDUCED SYNCHRONIZATION BY LARGE DELAY. 2021. ⟨hal-03183760⟩
64 Consultations
86 Téléchargements

Partager

Gmail Facebook X LinkedIn More