Periodic solutions in a model of recurrent neural feedback
SIAM Journal on Applied Mathematics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
Numerical methods for bifurcations of dynamical equilibria
Numerical methods for bifurcations of dynamical equilibria
Numerical bifurcation analysis of delay differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Collocation Methods for the Computation of Periodic Solutions of Delay Differential Equations
SIAM Journal on Scientific Computing
On Stability of LMS Methods and Characteristic Roots of Delay Differential Equations
SIAM Journal on Numerical Analysis
MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs
ACM Transactions on Mathematical Software (TOMS)
Numerical bifurcation analysis of immunological models with time delays
Journal of Computational and Applied Mathematics - Special issue: Mathematics applied to immunology
Solution operator approximations for characteristic roots of delay differential equations
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Efficient computation of characteristic roots of delay differential equations using LMS methods
Journal of Computational and Applied Mathematics
Solution operator approximations for characteristic roots of delay differential equations
Applied Numerical Mathematics
Bifurcation analysis of delay-induced periodic oscillations
Journal of Computational and Applied Mathematics
Numerical bifurcation analysis of immunological models with time delays
Journal of Computational and Applied Mathematics - Special issue: Mathematics applied to immunology
Automatica (Journal of IFAC)
SIAM Journal on Control and Optimization
A Krylov Method for the Delay Eigenvalue Problem
SIAM Journal on Scientific Computing
Stability of Neutral Systems with Commensurate Delays and Poles Asymptotic to the Imaginary Axis
SIAM Journal on Control and Optimization
Journal of Computational and Applied Mathematics
Matrix-free continuation of limit cycles for bifurcation analysis of large thermoacoustic systems
Journal of Computational Physics
Automatica (Journal of IFAC)
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We describe DDE-BIFTOOL, a Matlab package for numerical bifurcation analysis of systems of delay differential equations with several fixed, discrete delays. The package implements continuation of steady state solutions and periodic solutions and their stability analysis. It also computes and continues steady state fold and Hopf bifurcations and, from the latter, it can switch to the emanating branch of periodic solutions. We describe the numerical methods upon which the package is based and illustrate its usage and capabilities through analysing three examples: two models of coupled neurons with delayed feedback and a model of two oscillators coupled with delay.