# Persistence of Periodic Orbits under State-dependent Delayed Perturbations: Computer-assisted Proofs

@article{Gimeno2021PersistenceOP, title={Persistence of Periodic Orbits under State-dependent Delayed Perturbations: Computer-assisted Proofs}, author={Joan Gimeno and Jean‐Philippe Lessard and Jason D. Mireles-James and Jiaqi Yang}, journal={ArXiv}, year={2021}, volume={abs/2111.06391} }

A computer-assisted argument is given, which provides existence proofs for periodic orbits in state-dependent delayed perturbations of ordinary differential equations (ODEs). Assuming that the unperturbed ODE has an isolated periodic orbit, we introduce a set of polynomial inequalities whose successful verification leads to the existence of periodic orbits in the perturbed delay equation. We present a general algorithm, which describes a way of computing the coefficients of the polynomials and…

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