The EVF command creates a new vector field in which an existing vector field is extended with its variational equations.
Often it is useful to solve the variational equations of a vector field. One simple way to do this is to create a system consisting of the original vector field x'=F(x) and the variational equation dx' = DF(x)dx, where DF(x) is the Jacobian at x. (For example, this is the system created in the file with the suffix "_evf.m" in VFGEN's MATLAB command.) However, you will not have an explicit Jacobian of the extended system, unless you write the function yourself.
An alternative is to use the EVF command of VFGEN. The output of this command is a new vector field specification in which the original vector field has been extended with the variational equations. The new vector field is a 2N dimensional system that consists of the original vector field plus its variational equation. The symbols used for the extended variables are the same as the original variables with the letter "d" prepended to them. For example, if the original system uses the variables x and y, the new system will use x, y, dx, and dy. After running your vector field file through VFGEN to create the extended vector field, you can use VFGEN to output the extended system in the format of your choice, and you will automatically have the Jacobian(s) of the extended system.
par |
If the option par=p is given, where p is a Parameter,
the vector field is extended with the equations
Default: If the par option is not specified, the Jacobian with respect to a parameter is not added to DF(x)dx in the extended vector field. |
Here is an example of using the EVF command with the input vector field file pendulum.vf.
Note that, unlike most VFGEN commands, the ouput is sent to the console rather than a file. In this example, we have redirected the output to the file pendulum_evf.vf.