Delay Differential Equations

Delay differential equation initial value problem solvers

Delay differential equations contain terms whose value depends on the solution at prior times. The time delays can be constant, time-dependent, or state-dependent, and the choice of the solver function (dde23, ddesd, or ddensd) depends on the type of delays in the equation. Typically the time delay relates the current value of the derivative to the value of the solution at some prior time, but in the case of a neutral equation it can depend on the value of the derivative at prior times. Since the equations depend on the solution at prior times, it is necessary to provide a history function that conveys the value of the solution before the initial time t0. For more information, see Solving Delay Differential Equations.

Functions

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dde23Solve delay differential equations (DDEs) with constant delays
ddesdSolve delay differential equations (DDEs) with general delays
ddensdSolve delay differential equations (DDEs) of neutral type
ddegetExtract properties from delay differential equations options structure
ddesetCreate or alter delay differential equations options structure
devalEvaluate differential equation solution structure

Topics

Featured Examples

DDE with Constant Delays

DDE with Constant Delays

Use dde23 to solve a system of DDEs (delay differential equations) with constant delays.

DDE with State-Dependent Delays

DDE with State-Dependent Delays

Use ddesd to solve a system of DDEs (delay differential equations) with state-dependent delays. This system of DDEs was used as a test problem by Enright and Hayashi [1].

Cardiovascular Model DDE with Discontinuities

Cardiovascular Model DDE with Discontinuities

Use dde23 to solve a cardiovascular model that has a discontinuous derivative. The example was originally presented by Ottesen [1].

DDE of Neutral Type

DDE of Neutral Type

Use ddensd to solve a neutral DDE (delay differential equation), where delays appear in derivative terms. The problem was originally presented by Paul [1].

Initial Value DDE of Neutral Type

Initial Value DDE of Neutral Type

Use ddensd to solve a system of initial value DDEs (delay differential equations) with time-dependent delays. The example was originally presented by Jackiewicz [1].