Algorithms for determination of period-doubling bifurcation points in ordinary differential equations

DOI10.1016/0021-9991(87)90010-6zbMath0622.65069OpenAlexW2114316193MaRDI QIDQ1091086

Milan Kubiček, Martin Holodniok

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0021-9991(87)90010-6

zbMATH Keywords

periodic solutionsnonlinear dynamic systemsshooting methodLorenz modelautonomous systemFeigenbaum sequenceperiod-doubling bifurcation pointssystems of low order

Mathematics Subject Classification ID

Numerical methods for ordinary differential equations (65L99) Dynamical systems and ergodic theory (37-XX)

Related Items (5)

Periodic doubling solutions in the Duffing oscillator: A Galerkin approach ⋮ Characterization and computation of period doubling points by minimally exteded systems ⋮ Codimension-\(m\) bifurcation theorems applicable to the numerical verification methods ⋮ Spectral element method in time for rapidly actuated systems ⋮ A postverification method for solving forced Duffing oscillator problems without prescribed periods

Cites Work

• Numerical methods for bifurcation problems. Proceedings of the Conference at the University of Dortmund, August 22-26, 1983
• Period doubling bifurcations for families of maps on \(R^ n\)
• New algorithms for the evaluation of complex bifurcation points in ordinary differential equations. A comparative numerical study
• DERPER - An algorithm for the continuation of periodic solutions in ordinary differential equations
• Bifurcation and symmetry breaking in applied mathematics
• Deterministic Nonperiodic Flow
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
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