We know that famous Lorenz system firstly developed as a model for atmospheric convection. Is there any real data which can show that model is acceptable? There are 3 parameters in Lorenz equations which can make great qualitative changes (bifurcation) in the system time series. Is there any real data which can help us to estimate these parameters?
In almost all of the researches on parameter estimation of chaotic systems, there are no real data. In those researches both real system and model are exactly the same ODEs (or maps). Their difference is that the parameters are known in ODE (or map) who plays the role of real system, while the parameters supposed to be unknown in the other ODE (or map). I want to do the parameter estimation for a REAL system which has a valid model (since I don’t want to do system identification, I need a valid model which only needs parameter estimation). The only thing came to my mind was chaotic circuits, but I want something different. I am ready to collaborate on this topic if someone can provide me those data and valid model (map or flow, no difference). I think the possibility of finding discrete data which have a model in the form of map is more.
Thank you