The DDE23 function in MATLAB solves differential delay equations with constant lags.
A set of MATLAB files configured to use the DDE23
function are created by the command
The vector field must have at least one delay expression,
and the delay can not depend on the independent variable or on
any state variables.
The method by which parameters are passed to the MATLAB
functions generated by VFGEN is controlled by the
The default is parstyle=vector, and the alternative parameter style
is specifed with the option parstyle=list.
When parstyle=list is given as
$ vfgen dde23:parstyle=list vector_field_file.vfeach parameter is listed explicitly as an argument of MATLAB functions. That is, instead of
[name]_dde23(t,x,Zlags,p)the vector field function will be
If the option demo=yes is given, the file [name]_dde23_demo.m
is created. This MATLAB file defines the function
function [name]_dde23_demo(stoptime)which when called will solve the equations using DDE23 (with the default initial conditions and parameters) for the time interval 0 ≤ t ≤ stoptime.
The Mackey-Glass equation is
Here is the Mackey-Glass vector field file: MackeyGlass.vf.
The files created by
Here is the plot generated by the MATLAB command MackeyGlass_dde23_demo(500):
The SIR delay equations are
|S'(t)||=||-α S I|
|I'(t)||=||α (S I - S(t-τ) I(t-τ))|
|R'(t)||=||α S(t-τ) I(t-τ)|
These equations are a simple model of the spread of a disease in a well-mixed population in which each individual is infectious for exactly τ time units.
The file SIRdelay.vf is a vector field file for this system.
We create a MATLAB function that may be used with the DDE23 library with the command
The file SIRdelay_dde23_solver.m was written to use the DDE23 function generated by VFGEN to solve these equations.Here is the plot generated by the command SIRdelay_dde23_solver(50):