1 citations · 2 across the 5 of their papers we have counts for
5 papers
Persistence of hyperbolic solutions of ODE's under functional perturbations: Applications to the motion of relativistic charged particles
Joan Gimeno, Rafael de la Llave, Jiaqi Yang
We rigorously construct a variety of orbits for certain delay differential equations, including the electrodynamic equations formulated by Wheeler and Feynman in 1949. These equati…
Persistence of Periodic Orbits under State-dependent Delayed Perturbations: Computer-assisted Proofs
Joan Gimeno, Jean-Philippe Lessard, J. D. Mireles James +1
A computer-assisted argument is given, which provides existence proofs for periodic orbits in state-dependent delayed perturbations of ordinary differential equations (ODEs). Assum…
Persistence and Smooth Dependence on Parameters of Periodic Orbits in Functional Differential Equations Close to an ODE or an Evolutionary PDE
Jiaqi Yang, Joan Gimeno, Rafael de la Llave
We consider functional differential equations(FDEs) which are perturbations of smooth ordinary differential equations(ODEs). The FDE can involve multiple state-dependent delays or…
Numerical computation of periodic orbits and isochrons for state-dependent delay perturbation of an ODE in the plane
Joan Gimeno, Jiaqi Yang, Rafael de la Llave
We present algorithms and their implementation to compute limit cycles and their isochrons for state-dependent delay equations (SDDE's) which are perturbed from a planar differenti…
Parameterization method for state-dependent delay perturbation of an ordinary differential equation
Jiaqi Yang, Joan Gimeno, Rafael de la Llave
We consider state-dependent delay equations (SDDE) obtained by adding delays to a planar ordinary differential equation with a limit cycle. These situations appear in models of sev…