Stable periodic orbits for delay differential equations with unimodal feedback
G Benedek, T Krisztin, R Szczelina - Journal of Dynamics and Differential …, 2024 - Springer
We consider delay differential equations of the form\(y^{\prime}(t)=-ay (t)+ bf (y (t-1))\) with
positive parameters a, b and a unimodal\(f:[0,\infty)\rightarrow [0, 1]\). It is assumed that the …
positive parameters a, b and a unimodal\(f:[0,\infty)\rightarrow [0, 1]\). It is assumed that the …
High-order lohner-type algorithm for rigorous computation of Poincaré maps in systems of delay differential equations with several delays
R Szczelina, P Zgliczyński - Foundations of Computational Mathematics, 2024 - Springer
We present a Lohner-type algorithm for rigorous integration of systems of delay differential
equations (DDEs) with multiple delays, and its application in computation of Poincaré maps …
equations (DDEs) with multiple delays, and its application in computation of Poincaré maps …
Persistence of periodic orbits under state-dependent delayed perturbations: computer-assisted proofs
J Gimeno, JP Lessard, JD Mireles James… - SIAM Journal on Applied …, 2023 - SIAM
The goal of this study is to develop a computer-assisted method for proving the existence of
periodic solutions for state-dependent delayed perturbations of ordinary differential …
periodic solutions for state-dependent delayed perturbations of ordinary differential …
Periodic Orbits of State-Dependent Delay Differential Equations
N Corbett, V Naudot - International Journal of Bifurcation and Chaos, 2025 - World Scientific
In this work, we present a method to find periodic orbits for state-dependent delay differential
equations. This method is based on the Newton–Kantorovich algorithm and is illustrated in …
equations. This method is based on the Newton–Kantorovich algorithm and is illustrated in …