Detecting coupling in the presence of noise and nonlinearity.

*(English)* Zbl 1268.62129
Schelter, Björn (ed.) et al., Handbook of time series analysis: Recent theoretical developments and applications. Weinheim: Wiley-VCH (ISBN 978-3-527-40623-4/hbk; 978-3-527-60997-0/ebook). 265-282 (2006).

Summary: Establishing the presence of coupling and interactions in weakly coupled systems, especially in the presence of noise and nonlinearity, is a difficult problem. We explore different measures to detect a relationship between two systems. We compare the sensitivity of the different measures to stochastic coupled systems, discontinuous chaotic systems and continuous chaotic systems. We then test the robustness of the detection of coupling in the presence of additive noise. In conclusion, we find that nonlinear methods are more sensitive to detecting coupling under ideal conditions. However, in the presence of noise, linear techniques are more robust.

##### MSC:

62M99 | Inference from stochastic processes |

37N99 | Applications of dynamical systems |

37D45 | Strange attractors, chaotic dynamics |