Some Peculiarities of Causal Analysis of Coupled Chaotic Systems

On a test example of uni-directionally coupled Rössler systems we demonstrate some of the pitfalls of causal analysis of chaotic data. The method based on evaluating predictability in reconstructed state spaces is used here to detect causality. The results show that the predictability of the driven Rössler system is improved by incorporating information about the present state of the driver to the prediction process. The predictability improvement correctly reveals the presence and the direction of the coupling. However, causal analysis of the time-reversed test signals does not allow to uncover that the cause precedes the effect. In addition, causal analysis of complex systems may also encounter other complications such as transient chaos, or irreversibility of dissipative chaos sometimes masked by the dominance of limit cycles.