Application of the Liapunov–Floquet transformation to differential equations with time delay and periodic coefficients

DOI10.1177/1077546311433914zbMath1348.34117OpenAlexW2067625641MaRDI QIDQ2831937

Eric A. Butcher, Brian P. Mann, Oleg A. Bobrenkov

Publication date: 4 November 2016

Published in: Journal of Vibration and Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1177/1077546311433914

zbMATH Keywords

delay differential equationChebyshev collocationcontinuous time approximationLiapunov-Floquet transformation

Mathematics Subject Classification ID

Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Linear functional-differential equations (34K06) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (1)

On the robust stabilizability of unstable systems with feedback delay by finite spectrum assignment

Cites Work

• On the Chebyshev spectral continuous time approximation for constant and periodic delay differential equations
• Order reduction of retarded nonlinear systems - the method of multiple scales versus center-manifold reduction
• Dimensional reduction of nonlinear delay differential equations with periodic coefficients using Chebyshev spectral collocation
• Construction of dynamically equivalent time-invariant forms for time-periodic systems
• Symbolic computation of local stability and bifurcation surfaces for nonlinear time-periodic systems
• Estimating critical Hopf bifurcation parameters for a second-order delay differential equation with application to machine tool chatter
• Order reduction of parametrically excited nonlinear systems: Techniques and applications
• Order reduction of nonlinear systems with time periodic coefficients using invariant manifolds
• Semi-discretization method for delayed systems
• Control of chaos in nonlinear systems with time-periodic coefficients
• Error Bounds for Approximate Eigenvalues of Periodic-Coefficient Linear Delay Differential Equations
• Pseudospectral Differencing Methods for Characteristic Roots of Delay Differential Equations
• Subcritical Hopf bifurcation in the delay equation model for machine tool vibrations

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