Inconsistencies in Numerical Simulations of Dynamical Systems Using Interval Arithmetic

DOI10.1142/S0218127418500554zbMath1476.37093WikidataQ59899490 ScholiaQ59899490MaRDI QIDQ4643619

Matjaž Perc, Heitor M. jun. Rodrigues, Samir A. M. Martins, Márcia L. C. Peixoto, Erivelton Geraldo Nepomuceno

Publication date: 25 May 2018

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

chaosmodelingsimulationdynamical systemserror propagationinterval arithmeticinterval extensions

Mathematics Subject Classification ID

Simulation of dynamical systems (37M05) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50)

Related Items

Soft Computing Simulations of Chaotic Systems

Uses Software

• CoStLy
• C-XSC 2.0
• INTLAB

Cites Work

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• Single level constraint interval arithmetic
• Scientific computing with automatic result verification
• Do numerical orbits of chaotic dynamical processes represent true orbits?
• On the analysis of pseudo-orbits of continuous chaotic nonlinear systems simulated using discretization schemes in a digital computer
• Is an interval the right result of arithmetic operations on intervals?
• Quantitative universality for a class of nonlinear transformations
• Proving the existence of long periodic orbits in 1D maps using interval Newton method and backward shooting
• Can we trust in numerical computations of chaotic solutions of dynamical systems ?
• CoStLy: A Validated Library for Complex Functions
• A Very Simple Method to Calculate the (Positive) Largest Lyapunov Exponent Using Interval Extensions
• Introduction to Interval Analysis
• Nonlinear Behaviors of First and Second-Order Complex Digital Filters With Two's Complement Arithmetic
• Numerical Software with Result Verification
• Simple mathematical models with very complicated dynamics