How do numerical methods perform for delay differential equations undergoing a Hopf bifurcation?

DOI10.1016/S0377-0427(00)00473-8zbMath0971.65068OpenAlexW2067576443MaRDI QIDQ1841961

Volker Wulf, Neville J. Ford

Publication date: 18 February 2001

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

Full work available at URL: https://doi.org/10.1016/s0377-0427(00)00473-8

zbMATH Keywords

Hopf bifurcationdifference schemefixed-point iterationdelay differential equationsmesh refinementtheta method

Mathematics Subject Classification ID

Related Items (6)

NUMERICAL INVESTIGATION OF D-BIFURCATIONS FOR A STOCHASTIC DELAY LOGISTIC EQUATION ⋮ BIFURCATIONS IN NUMERICAL METHODS FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS ⋮ BIFURCATIONS IN APPROXIMATE SOLUTIONS OF STOCHASTIC DELAY DIFFERENTIAL EQUATIONS ⋮ Numerical treatment of oscillatory functional differential equations ⋮ Noise-induced changes to the behaviour of semi-implicit Euler methods for stochastic delay differential equations undergoing bifurcation ⋮ Retarded differential equations

Uses Software

• PDDE-CONT

Cites Work

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• Naimark-Sacker bifurcations in the Euler method for a delay differential equation
• Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations
• Introduction to functional differential equations
• The life-span of backward error analysis for numerical integrators
• Periodic orbits of delay differential equations under discretization
• Delay equations. Functional-, complex-, and nonlinear analysis
• The use of boundary locus plots in the identification of bifurcation points in numerical approximation of delay differential equations
• Numerical Hopf bifurcation for a class of delay differential equations
• Some Applications of the Boundary-Locus Method and the Method of D-Partitions
• Computation, Continuation and Bifurcation Analysis of Periodic Solutions of Delay Differential Equations
• Direct computation of period doubling bifurcation points of large-scale systems of ODEs using a Newton-Picard method
• Elements of applied bifurcation theory

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