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Data-driven stochastic simulation leading to the allometric scaling laws in complex systems

Yuh Kobayashi*

Hideki Takayasu†

Shlomo Havlin‡

Misako Takayasu§

  • Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8502, Japan

  • Sony Computer Science Laboratories, Tokyo 141-0022, Japan

  • Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel

  • Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8502, Japan

  • *Also at Department of Mathematical Sciences, College of Science and Engineering, Aoyama Gakuin University, Sagamihara 252-5258, Japan; kobayashi@math.aoyama.ac.jp
  • †Also at Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8502, Japan.
  • ‡Also at Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8502, Japan.
  • §Corresponding author: takayasu.m.aa@m.titech.ac.jp
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Phys. Rev. E 106, 064304 – Published 7 December, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.064304

Abstract

We propose a data-driven stochastic method that allows the simulation of a complex system's long-term evolution. Given a large amount of historical data on trajectories in a multi-dimensional phase space, our method simulates the time evolution of a system based on a random selection of partial trajectories in the data without detailed knowledge of the system dynamics. We apply this method to a large data set of time evolution of approximately one million business firms for a quarter century. Accordingly, from simulations starting from arbitrary initial conditions, we obtain a stationary distribution in three-dimensional log-size phase space, which satisfies the allometric scaling laws of three variables. Furthermore, universal distributions of fluctuation around the scaling relations are consistent with the empirical data.

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Phys. Rev. E 106, 064304– Published 7 December, 2022
  • Received 22 March 2022
  • Revised 15 September 2022
  • Accepted 19 September 2022
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