| Full text | |
| Author(s): |
Poignard, Camille
Total Authors: 1
|
| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 310, p. 555-601, FEB 15 2022. |
| Web of Science Citations: | 0 |
| Abstract | |
We investigate the dynamics of a delay differential equation obtained by perturbing a vector field f : Rn -> Rn, admitting a stable periodic orbit, by using a delayed feedback control term eta g(x, x(t - tau)) of same regularity, where eta is small and tau large so that eta tau be bounded but non small. We prove that trajectories starting in a neighborhood (of size independent of the parameters eta, tau) of this original periodic orbit enter asymptotically a periodic regime, and that the number of such distinct periodic regimes increases (almost) linearly when eta tau increases infinitely. Our result is based on the construction of an invariant manifold via a process inspired by the Lyapunov-Perron method for integral operators associated to 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 of delay differential equations. (c) 2021 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 17/21896-3 - Self-induced synchronization by strong delay in complex networks |
| Grantee: | Camille Poignard |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |