Information Transfer -- A Rigorous Formalism
X. San Liang
Courant Institute of Mathematical Sciences
Last modified: June 28, 2007
We put the concept of information transfer on a rigorous footing and establish for it a formalism within the framework of dynamical systems. The resulting transfer measure possesses the desired property of causality; it also verifies the transfer measure for 2D systems, which was obtained by Liang and Kleeman (2005) through a different avenue. Connections to classical formalisms are explored and applications presented. We find that, in the context of the baker transformation, there is always information flowing from the stretching direction to the folding direction, while no transfer occurs in the opposite direction; we also find that, within the Henon map system, the transfer from the quadratic component to the linear component is of a simple form as expected on physical grounds. Application to a two-mode (4D) truncated Burgers-Hopf system reveals that siginificant transfer only exists between the cosine direction of mode 2 and the sine direction of mode 1, and that the transfer occurs continuously and at a nearly constant rate.
Key words: Information flow, Causality, Frobenius-Perron operator, Baker transformation, Henon map, truncated Burgers-Hopf system.
Liang and Kleeman, Phys. Rev. Lett., 95, No. 24, 244101 (2005).
Liang and Kleeman, Physica D, 231, 1-9 (2007).
Liang and Kleeman, Physica D, 227, 173-182 (2007).