Chaos Identification and Prediction Methods

Abstract

Considerable interest in studying the chaotic behavior of natural, physical, and socio-economic systems have led to the development of many different methods for identification and prediction of chaos. An important commonality among almost all of these methods is the concept of phase space reconstruction. Other than this, the methods largely have different bases and approaches and often aim to identify different measures of chaos. All these methods have been successfully applied in many different scientific fields. This chapter describes some of the most popular methods for chaos identification and prediction, especially those that have found applications in hydrology. These methods include: phase space reconstruction, correlation dimension method, false nearest neighbor method, Lyapunov exponent method, Kolmogorov entropy method, surrogate data method, Poincare maps, close returns plot, and nonlinear local approximation prediction method. To put the utility of these methods in a proper perspective in the identification of chaos, the superiority of two of these methods (phase space reconstruction and correlation dimension) over two commonly used linear tools for system identification (autocorrelation function and power spectrum) is also demonstrated. Further, as the correlation dimension method has been the most widely used method for chaos identification, it is discussed in far more detail.