# 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

expand all

 `dde23` Solve delay differential equations (DDEs) with constant delays `ddesd` Solve delay differential equations (DDEs) with general delays `ddensd` Solve delay differential equations (DDEs) of neutral type
 `ddeget` Extract properties from delay differential equations options structure `ddeset` Create or alter delay differential equations options structure
 `deval` Evaluate differential equation solution structure

## Topics

• Solving Delay Differential Equations

Background information, solver capabilities and algorithms, and example summary.

• DDE with Constant Delays

This example shows how to use `dde23` to solve a system of DDEs (delay differential equations) with constant delays.

• DDE with State-Dependent Delays

This example shows how to use `ddesd` to solve a system of DDEs (delay differential equations) with state-dependent delays.

• Cardiovascular Model DDE with Discontinuities

This example shows how to use `dde23` to solve a cardiovascular model that has a discontinuous derivative.

• DDE of Neutral Type

This example shows how to use `ddensd` to solve a neutral DDE (delay differential equation), where delays appear in derivative terms.

• Initial Value DDE of Neutral Type

This example shows how to use `ddensd` to solve a system of initial value DDEs (delay differential equations) with time-dependent delays.