Note: PDDE-CONT has been superceded by Knut. The VFGEN command for PDDE-CONT is now unsupported, and it may be removed in a future version.
PDDE-CONT is a software package developed by Róbert Szalai for continuation and bifurcation analysis of periodic solutions to delay differential equations.
A C++ system definition file for the PDDE-CONT package
is created by the command
The vector field must have at least one delay expression.
The file ShayerCampbell2000.vf defines the following system of equations:
|x1'(t)||=||-κ x1(t) + β tanh(x1(t-τs)) + a12 tanh(x2(t-τ2))|
|x2'(t)||=||-κ x2(t) + β tanh(x2(t-τs)) + a21 tanh(x1(t-τ1))|
This example was taken from the DDE-BIFTOOL manual. The reference given there for these equations is:
This example uses these constants files:
The equation is not a delay equation; this example is simply a test of using PDDE-CONT to compute a family of solutions to a periodic vector field.
This equation can be written as the system
|y '||=||-x - ε y - ε x3 + ε a cos(ω t )|
|y '(θ)||=||T [-x - ε y - ε x3 + ε a cos(2π θ )]|
|x||=||1.85 cos(θ - 0.34)|
|y||=||1.79 cos(θ + 1.2)|
We create a system definition file for PDDE-CONT with the command
We use the constants files
Finally, we use the MATLAB script wnplot.m to create the following graph of the amplitude of the periodic orbit as a function of ω.