Toy Model
We use the toy model in [POR20] to demonstrate
the use of resolvent4py to perform the harmonic resolvent analysis.
The governing equations are
\[\begin{split}\begin{align} \dot{x} &= \mu x - \gamma y - \alpha x z - \beta x y\\ \dot{y} &= \gamma x + \mu y - \alpha y z + \beta x^2\\ \dot{z} &= -\alpha z + \alpha (x^2 + y^2) \end{align}\end{split}\]
with parameters \((\alpha, \beta, \gamma, \mu) = (1/5, 1/5, 1, 1/5)\). For this choice of parameters, the origin is unstable and the state will settle onto a time-periodic limit cycle. We linearize the equations about this time-periodic solution and perform the harmonic resolvent analysis as in [POR20].
Instructions
Generate the blocks of the harmonic balanced matrix using
mpiexec -n 1 python -u generate_matrices.py
This script must be run in series, and its outputs will be written in
data/.Run harmonic resolvent analysis with
mpiexec -n 2 python -u demonstrate_harmonic_resolvent.py
This script can be run with any number of processors (although the dimension of the system is rather small, so there might not be any benefit in running it in parallel).
Navigate to the
results/directory to check out the results.
