A Topological View of Chaos : (I) Application to a Daily Streamflow Analysis
Kim Hung Soo, Yoon Yong Nam · Journal of the Korean Society of Civil Engineers · 1996
While the metric approaches such as correlation dimension and the largest Lyapunov exponent have been mostly used to distinguish chaos from stochastic system, and they are becoming the standard rules for testing chaotic behavior of a scalar time series, some studies have recently developed topological techniques for testing deterministic chaos. Relatively, topological techniques require small data set and easy implementation. This paper applies one of topological methodologies called the close returns test which has successful applications in physics and in the economic data sets to a daily streamflow time series for testing the deterministic chaos. The result by a topological technique is compared with those of metric approaches. In our analysis, a daily streamflow based on the metric approaches represents its chaotic behavior, but the deterministic chaos is rejected from a topopogical technique. The close returns test shows the periodic pattern of a daily streamflow and it may be considered that the periodic stochastic models are more appropriate for a daily streamflow applied in this study.