The Effects of Dynamical Noises on the Identification of Chaotic Systems: with Application to Streamflow Processes

Three known chaotic system corrupted with different levels of dynamic noise were investigated for assessing the effects of dynamical noises on the identification of chaotic systems. It is found that when noise level is low, the chaotic attractor can still be well preserved and we can give basically correct estimate of correlation dimension, which indicates that even if we observed the existence of chaos in a time series, it does not necessarily mean determinism. On the other hand, in the presence of high-level dynamical noise, it is hard or even impossible to identify a chaotic system. Two streamflow processes are investigated as well for detecting the existence of chaotic behaviour. The existence of low-dimensional chaos in the streamflow series is not confirmed with the method of correlation dimension. Because the streamflow process usually suffers from strong natural and anthropogenic disturbances which are composed of both stochastic and deterministic components, consequently, it is not likely to identify the chaotic dynamics even if the streamflow process is indeed a low-dimension chaotic process under ideal circumstances (i.e., without any or only with small enough stochastic disturbances).