Delay Differential Equations
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
Topics
- Solving Delay Differential Equations
Background information, solver capabilities and algorithms, and example summary.
Featured Examples
DDE with Constant Delays
Use dde23 to solve a system of DDEs (delay differential equations) with constant 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
Use dde23 to solve a cardiovascular model that has a discontinuous derivative. The example was originally presented by Ottesen [1].
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
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].
