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An improving method for inferring interactions of nonlinear systems with linearizable hidden variables

  • Regular Article - Statistical and Nonlinear Physics
  • Published:
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Abstract

Detecting the interactions in a network from measurable data is a challenging practical issue. In real systems, the state variables are not only affected by their local dynamics and coupling functions, but also by unknown effects, i.e., hidden variables. Many researchers have studied complex networks containing hidden variables. Shi et al. proposed a method to reconstruct the interactions in dynamic systems with hidden variables, which, however, exhibited large errors in reconstructing strongly nonlinear systems. In this paper, we proposed an improved method for reconstructing the systems with linearized hidden variables by introducing expanded variables and best square approximation and compared it with the original method. The comparison results show that our improving method can effectively enhance the accuracy of detecting the interactions in strongly nonlinear systems and reduce the reconstruction error of corresponding coefficients. Numerical simulation results also verify the robustness of our method in reconstructing strongly nonlinear systems. In addition, we also discussed the main influencing parameters of the method.

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Data Availability Statement

The manuscript has associated data in a data repository. [Authors’ comment: The data that support the findings of this study are available from the corresponding author upon reasonable request.]

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Authors and Affiliations

  1. School of Sciences, Beijing University of Posts and Telecommunications, Beijing, 100876, People’s Republic of China

    Weinuo Jiang, Zhitao Wang & Shihong Wang

Authors
  1. Weinuo Jiang
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  2. Zhitao Wang
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  3. Shihong Wang
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Contributions

All authors were involved in the preparation of the theoretical derivation and numerical simulations of the manuscript, as well as in the reading and confirmation of the final manuscript.

Corresponding author

Correspondence to Shihong Wang.

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Jiang, W., Wang, Z. & Wang, S. An improving method for inferring interactions of nonlinear systems with linearizable hidden variables. Eur. Phys. J. B 94, 138 (2021). https://doi.org/10.1140/epjb/s10051-021-00148-1

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  • DOI: https://doi.org/10.1140/epjb/s10051-021-00148-1

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