Hi, I’m trying to figure out a way to compare how fast the oscillations in two ODE models decay. For example, the two figures below show the solution of a model that differs only in temperature, and I want to be able to say something like “the model stabilizes faster at higher temperatures” or vis …

[image] ANasc: I’m trying to figure out a way to compare how fast the oscillations in two ODE models decay. This sounds like the sort of thing you could do via linearization, if the ODE models are time-invariant. That is, if you have an ODE like dx/dt = f(x), then in the limit of small \Vert…

This sounds like a great idea. I will give it a try as soon as I can. Thanks!

Another approach would be to fit an exponentially damped sinusoid to your data using e.g. Prony’s Method

[image] ANasc: Perhaps there is a way to fit a negative exponential to the peaks or something? You could also check this other post about computing the Hilbert envelop.

This turned out to be a great solution, thank you! For those interested, I ended up doing this to get the eigenvalue with largest real part.: using ForwardDiff, NonlinearSolve function stability(inits, parameters) #initial conditions and parameters NLprob = NonlinearProblem(Alpha…

Thanks for the other suggestions as well. I’ve never heard of Prony’s Method or the Hilbert Envelope, but these are good to know about and could come in handy in the future.

[image] ANasc: eigen(J).values Minor side note: If you only care about the eigenvalues, I would recommend using eigvals(J) rather than eigen(J).values. The reason is that there are more efficient algorithms to compute just the eigenvalues (eigvals) than to compute both eigenvalues and eigenv…

For my own edification, I decided to try to implement what I suggested. I used the matrix pencil algorithm from this paper , which is said to be superior to Prony’s method, after translating the code from Matlab to Julia. I tried fitting a pair (p=2) of complex exponential functions (because the or…

That’s a very interesting method! It may come in handy at some point. Thanks for sharing!

One quick follow up question, if you don’t mind. Is it possible to obtain information on the amplitude of oscillations from the eigenvalues/vectors of the Jacobian in this case?

This will depend on the initial condition

Quantifying "damping" rate of ODE

General Usage

rafael.guerra December 6, 2022, 2:46pm 5

You could also check this other post about computing the Hilbert envelop.

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Quantifying "damping" rate of ODE

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