Algorithm for rigorous integration of delay differential equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation

DOI10.1007/s10208-017-9369-5zbMath1402.65050arXiv1607.01080OpenAlexW2962849511WikidataQ59610531 ScholiaQ59610531MaRDI QIDQ1620885

Robert Szczelina, Piotr Zgliczyński

Publication date: 14 November 2018

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.01080

zbMATH Keywords

interval arithmeticperiodic orbitdelay differential equationstopological methodscomputer-assisted proofs

Mathematics Subject Classification ID

Related Items (12)

A general method for computer-assisted proofs of periodic solutions in delay differential problems ⋮ Parameterization method for unstable manifolds of delay differential equations ⋮ Validated integration of differential equations with state-dependent delay ⋮ A rigorous implicit \(C^1\) Chebyshev integrator for delay equations ⋮ Persistence and smooth dependence on parameters of periodic orbits in functional differential equations close to an ODE or an evolutionary PDE ⋮ Traveling wave solutions for the FPU chain: a constructive approach ⋮ Distribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the Hénon-Heiles system ⋮ Torus knot choreographies in the n-body problem ⋮ Using automatic differentiation to compute periodic orbits of delay differential equations ⋮ Configurations of periodic orbits for equations with delayed positive feedback ⋮ Stable periodic orbits for the Mackey-Glass equation ⋮ Numerical inclusion of exact periodic solutions for time delay Duffing equation

Uses Software

• CAPD
• RODES

Cites Work

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