Implementation Issues
In some situation the model is not very efficient and difficulties can arise if the model has a large number of coefficients and demonstrates a divergent solution. For example, nonautonomous differential equations give the previously described results. In this case the modification of the standard approach in application gives a better way of further development of global vector reconstruction.
Usually the system being modeled in this way is a chaotic dynamical system, because chaotic systems explore a large part of the phase space and the estimate of the global dynamics based on the local dynamics will be better than with a system exploring only a small part of the space.
Frequently, one has only a single scalar time series measurement from a system known to have more than one degree of freedom. The time series may not even be from a system variable, but may be instead of a function of all the variables, such as temperature in a stirred tank reactor using several chemical species. In this case, one must use the technique of delay coordinate embedding, where a state vector consisting of the data at time t and several delayed versions of the data is constructed.
A comprehensive review of the topic is available from
Read more about this topic: Vector Field Reconstruction
Famous quotes containing the word issues:
“The current flows fast and furious. It issues in a spate of words from the loudspeakers and the politicians. Every day they tell us that we are a free people fighting to defend freedom. That is the current that has whirled the young airman up into the sky and keeps him circulating there among the clouds. Down here, with a roof to cover us and a gasmask handy, it is our business to puncture gasbags and discover the seeds of truth.”
—Virginia Woolf (1882–1941)