A general framework for validated continuation of periodic orbits in systems of polynomial ODEs

DOI10.3934/jcd.2021004zbMath1469.37015OpenAlexW3092818401MaRDI QIDQ2026919

Elena Queirolo, Jan Bouwe Van Den Berg

Publication date: 21 May 2021

Published in: Journal of Computational Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jcd.2021004

zbMATH Keywords

periodic orbitscontinuationsolution branchvalidated numericspolynomial ODEs

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) General methods in interval analysis (65G40) Periodic orbits of vector fields and flows (37C27) Computational methods for invariant manifolds of dynamical systems (37M21)

Related Items (7)

Existence of traveling wave solutions for the Diffusion Poisson Coupled Model: a computer-assisted proof ⋮ A constructive proof of the Cauchy-Kovalevskaya theorem for ordinary differential equations ⋮ When does the method of harmonic balance give a correct prediction for mechanical systems? ⋮ A Posteriori Validation of Generalized Polynomial Chaos Expansions ⋮ From the Lagrange polygon to the figure eight. I: Numerical evidence extending a conjecture of Marchal ⋮ Validated computations for connecting orbits in polynomial vector fields ⋮ Rigorous Verification of Hopf Bifurcations via Desingularization and Continuation

Uses Software

• MATCONT
• Matlab
• AUTO
• INTLAB
• AUTO-07P
• XPPAUT
• COCO
• PyDSTool
• CAPD
• galepu
• CkAnalytic

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