Information transfer at multiple scales

In the study of complex systems a fundamental issue is the mapping of the networks of interaction between constituent subsystems of a complex system or between multiple complex systems. Such networks define the web of dependencies and patterns of continuous and dynamic coupling between the system's elements characterized by directed flow of information spanning multiple spatial and temporal scales. Here, we propose a wavelet-based extension of transfer entropy to measure directional transfer of information between coupled systems at multiple time scales and demonstrate its effectiveness by studying (a) three artificial maps, (b) physiological recordings, and (c) the time series recorded from a chaos-controlled simulated robot. Limitations and potential extensions of the proposed method are discussed.