TY - JOUR

T1 - A rigorous formalism of information transfer between dynamical system components. II. Continuous flow

AU - Liang, X. San

AU - Kleeman, Richard

N1 - Funding Information:
XSL first learned about the remarkable stochastic dynamics of the truncated Burgers–Hopf system from Andrew Majda, whom he sincerely thanks. The intuitive thoughts from a referee on the possible relation between information exchange and the decouplability of dynamical system variables are greatly appreciated. This work was supported by NSF under CMG Grant 0417728 to Courant Institute of Mathematical Sciences.

PY - 2007/3/15

Y1 - 2007/3/15

N2 - The transfer of information between dynamical system components is formalized with causality faithfully represented. In a continuous system with many components, information transfer is a mechanism controlling the marginal entropy evolution of the target component. It is measured by the rate of entropy thus transferred, which is obtained through freezing the source component instantaneously, and comparing the entropy increases between the original system and the so modified system. The resulting transfer measure is consistent with our earlier 2D formalism derived in Liang and Kleeman [X.S. Liang, R. Kleeman, Information transfer between dynamical system components, Phys. Rev. Lett. 95 (24) (2005) 244101] using different methods; it also possesses a property of unidirectionalism which has been emphasized by Schreiber [T. Schreiber, Measuring information transfer, Phys. Rev. Lett. 85 (2) (2000) 461-464]. We apply our formalism to a two-mode (four-dimensional) truncated Burgers-Hopf system. No significant information exchange is identified between the four components, save for a transfer from the cosine direction of mode 2 to the sine direction of mode 1. This transfer occurs continuously and at a nearly constant rate. The present work should serve as a starting point for the development of a rigorous dynamics-free formalism for the information transfer of multivariate time series.

AB - The transfer of information between dynamical system components is formalized with causality faithfully represented. In a continuous system with many components, information transfer is a mechanism controlling the marginal entropy evolution of the target component. It is measured by the rate of entropy thus transferred, which is obtained through freezing the source component instantaneously, and comparing the entropy increases between the original system and the so modified system. The resulting transfer measure is consistent with our earlier 2D formalism derived in Liang and Kleeman [X.S. Liang, R. Kleeman, Information transfer between dynamical system components, Phys. Rev. Lett. 95 (24) (2005) 244101] using different methods; it also possesses a property of unidirectionalism which has been emphasized by Schreiber [T. Schreiber, Measuring information transfer, Phys. Rev. Lett. 85 (2) (2000) 461-464]. We apply our formalism to a two-mode (four-dimensional) truncated Burgers-Hopf system. No significant information exchange is identified between the four components, save for a transfer from the cosine direction of mode 2 to the sine direction of mode 1. This transfer occurs continuously and at a nearly constant rate. The present work should serve as a starting point for the development of a rigorous dynamics-free formalism for the information transfer of multivariate time series.

KW - Causality

KW - Continuous dynamical system

KW - Entropy evolution

KW - Information transfer

KW - Truncated Burgers-Hopf system

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U2 - 10.1016/j.physd.2006.12.012

DO - 10.1016/j.physd.2006.12.012

M3 - Article

AN - SCOPUS:33947603994

VL - 227

SP - 173

EP - 182

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 2

ER -