On rigorous integration of continuous piecewise linear systems

DOI10.1016/j.cnsns.2021.106109zbMath1490.37102OpenAlexW3212447333MaRDI QIDQ2074155

Zbigniew Galias

Publication date: 4 February 2022

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2021.106109

zbMATH Keywords

computer-assisted proofpiecewise linear systemChua's circuitrigorous numerical analysis

Mathematics Subject Classification ID

Analytic circuit theory (94C05) Discontinuous ordinary differential equations (34A36) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Numerical chaos (65P20) Computational methods for bifurcation problems in dynamical systems (37M20) Numerical nonlinear stabilities in dynamical systems (65P40) Computational methods for attractors of dynamical systems (37M22)

Uses Software

• CAPD DynSys

Cites Work

• Rigorous numerics for piecewise-smooth systems: a functional analytic approach based on Chebyshev series
• Derived eigenvalues of symmetric matrices, with applications to distance geometry
• A Lohner-type algorithm for control systems and ordinary differential inclusions
• CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems
• Solving Ordinary Differential Equations I
• A chaotic attractor from Chua's circuit
• Canonical realization of Chua's circuit family
• The double scroll family
• Reality of chaos in the double scroll circuit: A computer-assisted proof
• The Lorenz attractor exists
• Positive Topological Entropy of Chua's Circuit: A Computer Assisted Proof
• Rigorous Study of the Chua's Circuit Spiral Attractor
• FITTING TRAPPING REGIONS FOR CHUA'S ATTRACTOR — A NOVEL METHOD BASED ON ISOCHRONIC LINES
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