Software for delay differential equations

• TIME INTEGRATION

  • Archi (contact C.A.H. Paul) simulates a large class of functional differential equations.
  • dde23 (contact L. Shampine, S. Thompson) simulates retarded differential equations with several fixed discrete delays.
  • RADAR5 (contact N. Guglielmi, E. Hairer) simulates stiff problems, including differential-algebraic and neutral delay equations with constant or state-dependent (eventually vanishing) delay.
  • DKLAG6 (contact S. Thompson) simulates retarded and neutral differential equations with state dependent delays.
  • DDE_SOLVER (contact L. Shampine, S. Thompson) Fortran 90 DDE solver based on DKLAG6; what is new, look here.
  • RETARD (contact E. Hairer, G. Wanner) simulates retarded differential equations with several fixed discrete delays.
  • DDVERK (contact H. Hayashi, W. Enright) simulates retarded and neutral differential equations with several fixed discrete delays.
  • XPPAUT (contact G.B. Ermentrout) simulates differential equations with several fixed discrete delays.
  • Dynamics Solver (contact J. M. Aguirregabiria) simulates differential equations with discrete possibly varying delays.
  • DifEqu (contact G. Makay) simulates differential equations with discrete possibly varying delays.
  • Solv95 (contact S. N. Wood) simulates differential equations with discrete delays (for Windows operating systems).
  • DifferentialEquations.jl (contact Christopher Rackauckas), a suite of differential equation solvers in Julia that includes submodules like DelayDiffEq.jl, which uses a MethodOfSteps setup with fast Runge-Kutta and Rosenbrock methods to solve DDes.
  
  

• BIFURCATION ANALYSIS

  • DDE-BIFTOOL (started as a part of the PhD of K. Engelborghs, contact ddebiftool) allows computation and stability analysis of steady state solutions, their fold and Hopf bifurcations and periodic solutions of differential equations with several fixed discrete delays.
  • XPPAUT (see above) allows limited stability analysis of steady state solutions of differential equations with several fixed discrete delays.
  • BIFDD (contact B.D. Hassard) allows normal form analysis of Hopf bifurcations of differential equations with several fixed discrete delays.
  • Software for the computation of 1D unstable manifolds in DDEs (contact K. Green)
  • TRACE-DDE (contact D. Breda) allows to compute characteristic roots and stability charts in two parameters.
  • knut (contact R. Szalai) allows to perform continuation of periodic solution bifurcations.
  
  

• CONTROL DESIGN

  See the separate page.
  
  

• PARAMETER ESTIMATION (FITTING)

  • DDEfit (contact S. N. Wood) a Windows package that allows you to fit dynamic models specified as delay differential equations, differential equations or difference equations to data.
  
  Most of the above packages have additional capabilities for other types of equations or analysis, see their respective home pages for more details.
  More links to available software for dynamical systems (including some of the above) can be found at the Dynamical Systems Sofware page.
  
  Please mail ddebiftool if you are aware of any delay software not listed above.
  
  

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  Last modified June 27, 2013