Parameter estimation for Chaotic or Stochastic Dynamics
Sebastian, Springer (2016)
Diplomityö
Sebastian, Springer
2016
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe201603308915
https://urn.fi/URN:NBN:fi-fe201603308915
Tiivistelmä
Since its discovery, chaos has been a very interesting and challenging topic of research.
Many great minds spent their entire lives trying to give some rules to it. Nowadays,
thanks to the research of last century and the advent of computers, it is possible to
predict chaotic phenomena of nature for a certain limited amount of time.
The aim of this study is to present a recently discovered method for the parameter estimation of the chaotic dynamical system models via the correlation integral likelihood,
and give some hints for a more optimized use of it, together with a possible application
to the industry.
The main part of our study concerned two chaotic attractors whose general behaviour
is diff erent, in order to capture eventual di fferences in the results. In the various
simulations that we performed, the initial conditions have been changed in a quite
exhaustive way.
The results obtained show that, under certain conditions, this method works very well
in all the case. In particular, it came out that the most important aspect is to be
very careful while creating the training set and the empirical likelihood, since a lack of
information in this part of the procedure leads to low quality results.
Many great minds spent their entire lives trying to give some rules to it. Nowadays,
thanks to the research of last century and the advent of computers, it is possible to
predict chaotic phenomena of nature for a certain limited amount of time.
The aim of this study is to present a recently discovered method for the parameter estimation of the chaotic dynamical system models via the correlation integral likelihood,
and give some hints for a more optimized use of it, together with a possible application
to the industry.
The main part of our study concerned two chaotic attractors whose general behaviour
is diff erent, in order to capture eventual di fferences in the results. In the various
simulations that we performed, the initial conditions have been changed in a quite
exhaustive way.
The results obtained show that, under certain conditions, this method works very well
in all the case. In particular, it came out that the most important aspect is to be
very careful while creating the training set and the empirical likelihood, since a lack of
information in this part of the procedure leads to low quality results.