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

The goal of this study is to develop a computer-assisted method for proving the existence periodic solutions state-dependent delayed perturbations ordinary differential equations (ODEs). We assume that unperturbed ODE has an isolated orbit, and derive set polynomial inequalities which, if satisfied, imply uniqueness solution in perturbed system. A general procedure given, which facilitates computation coefficients optimization inputs necessary satisfy on explicit range perturbing parameter. Our approach uses tools from validated numerics interval arithmetic together with Chebyshev series expansions obtain orbit as well variational equations. illustrated by some orbits van der Pol equation.