One-dimensional unstable eigenfunction and manifold computations in delay differential equations

DOI10.1016/j.jcp.2003.11.018zbMath1052.65115OpenAlexW2170357931MaRDI QIDQ598127

Kirk Green, Bernd Krauskopf, Koen Engelborghs

Publication date: 6 August 2004

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

Full work available at URL: https://research-information.bris.ac.uk/ws/files/2988854/udp_main_rev4.pdf

zbMATH Keywords

numerical examplechaosdelay differential equationPoincaré mapsemiconductor laserunstable manifoldsIntermittent transitionPCF lasersaddle periodic orbitunstable eigenfunctions

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Periodic orbits of vector fields and flows (37C27) Computational methods for bifurcation problems in dynamical systems (37M20) Numerical bifurcation problems (65P30) Bifurcation theory of functional-differential equations (34K18) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

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Uses Software

• DDE-BIFTOOL

Cites Work

• Bistability and torus break-up in a semiconductor laser with phase-conjugate feedback
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• Bifurcation Analysis of Frequency Locking in a Semiconductor Laser with Phase-Conjugate Feedback
• One-Parameter Semigroups for Linear Evolution Equations
• A Two-Parameter Study of the Locking Region of a Semiconductor Laser Subject to Phase-Conjugate Feedback
• COMPUTING FLOQUET MULTIPLIERS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS
• Globalizing Two-Dimensional Unstable Manifolds of Maps
• Numerical bifurcation analysis of delay differential equations arising from physiological modeling