Numerical bifurcation analysis of delay differential equations

DOI10.1016/S0377-0427(00)00472-6zbMath0970.65090MaRDI QIDQ1841959

Dirk Roose, Koen Engelborghs, Tatyana Luzyanina

Publication date: 18 February 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

stabilityperiodic solutionsbifurcationneutral typesystems of delay differential equations

Mathematics Subject Classification ID

Related Items (17)

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Uses Software

• DDE-BIFTOOL
• PDDE-CONT

Cites Work

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• Effective computation of periodic orbits and bifurcation diagrams in delay equations
• On the zeros of exponential polynomials
• Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations
• Introduction to functional differential equations
• Parameter domains for instability of uniform states in systems with many delays
• Retarded differential equations
• Introduction to the theory and application of differential equations with deviating arguments. Translated from the Russian by John L. Casti
• Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations
• Numerical Hopf bifurcation for a class of delay differential equations
• Collocation Methods for the Computation of Periodic Solutions of Delay Differential Equations
• Periodic Solutions in a Model of Recurrent Neural Feedback
• A FitzHugh Differential-Difference Equation Modeling Recurrent Neural Feedback
• Computation, Continuation and Bifurcation Analysis of Periodic Solutions of Delay Differential Equations
• Sensitivity to Infinitesimal Delays in Neutral Equations
• Smoothness loss of periodic solutions of a neutral functional differential equation: On a bifurcation of the essential spectrum
• Matrix transformations for computing rightmost eigenvalues of large sparse non-symmetric eigenvalue problems
• Bifurcation Analysis of Periodic Solutions of Neural Functional Differential Equations: A Case Study

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