Model free modeling of agricultural and ecological dynamics from very short but ensemble time series data set based on the time delay embedding technique

Biological and ecological time series data are usually limited to their time direction, because the most of crop productions are scheduled in year domain. The nonlinear time series analysis has been developed to distinguish deterministic chaos from noisy time series for the last two decades. However, the methodology requires thousands of data size for their target time series data set. In this tutorial, the outline of the nonlinear time series analysis scheme consisting of time delayed embedding technique, correlation dimension analysis, Lyapunov exponent analysis, nonlinear deterministic prediction etc. is introduced. As a part of tutorial session, the author explains the general scheme of nonlinear time series analysis with a few case studies. Based on the scheme, the author tries to expand it to very short but ensemble ecological time series data set.