A database of rigorous and high-precision periodic orbits of the Lorenz model

DOI10.1016/j.cpc.2015.04.007zbMath1344.37002OpenAlexW2095587901MaRDI QIDQ312809

Roberto Barrio, Warwick Tucker, Angeles Dena

Publication date: 9 September 2016

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2015.04.007

zbMATH Keywords

periodic orbitscomputer-assisted proofLorenz modelvalidated numericshigh-precision

Mathematics Subject Classification ID

Related Items (10)

Topological classification of periodic orbits in the generalized Lorenz-type system with diverse symbolic dynamics ⋮ Algorithms for concatenating templates ⋮ Systematic Computer-Assisted Proof of Branches of Stable Elliptic Periodic Orbits and Surrounding Invariant Tori ⋮ The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension ⋮ Finding First Foliation Tangencies in the Lorenz System ⋮ Pure quadratization and solution of ordinary differential equations by probabilistic evolution theory with concurrent computation of coefficients using exact arithmetic ⋮ Heterogeneity of the attractor of the Lorenz '96 model: Lyapunov analysis, unstable periodic orbits, and shadowing properties ⋮ Visualizing the template of a chaotic attractor ⋮ Rigorous numerics for ODEs using Chebyshev series and domain decomposition ⋮ Coexistence and Dynamical Connections between Hyperchaos and Chaos in the 4D Rössler System: A Computer-Assisted Proof

Uses Software

• MPFR
• TIDES
• CAPD
• Lorenz-Database
• RODES

Cites Work

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• NUMERICAL STUDY OF COEXISTING ATTRACTORS FOR THE HÉNON MAP
• Topological analysis of chaotic dynamical systems
• Solving Ordinary Differential Equations I
• Algorithm 924
• MPFR
• Interval Methods for Systems of Equations
• The Lorenz attractor exists
• Chaos in the Lorenz equations: a computer-assisted proof
• Deterministic Nonperiodic Flow

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