Abstract
A computer assisted proof of multiple periodic orbits in some first order non-linear delay differential equation
Highlights
In this work we are dealing with the delay differential equation (DDE) of the form: x(t) = −μ · x(t) + λ · x(t − 1) · (1 + x(t − 1)), x ∈ R
Szczelina which was named there as so-called “logistic” DDE, as it is obtained by a singular perturbation limit procedure on the famous logistic map [16]
There are several papers that deal with computer assisted proofs of periodic solutions to DDEs [12, 13, 28], their approach is very different from our method
Summary
There are several papers that deal with computer assisted proofs of periodic solutions to DDEs [12, 13, 28], their approach is very different from our method These works transform the question of the existence of periodic orbits into a boundary value problem (BVP). The authors of [3] use the validated numerical integration to obtain the bounds of the solution only over a fixed interval and it is not clear if their method may be adopted to construct Poincaré maps.
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