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Phys. Rev. Lett. 80, 1385 - 1388 (1998)

Power Law Scaling for a System of Interacting Units with Complex Internal Structure

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Luís A. Nunes Amaral1,2, Sergey V. Buldyrev2, Shlomo Havlin2,3, Michael A. Salinger4, and H. Eugene Stanley2
1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
2Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215
3Minerva Center and Department of Physics, Bar-Ilan University, Ramat Gan, Israel
4Department of Finance and Economics, School of Management, Boston University, Boston, Massachusetts 02215

Received 28 July 1997; revised 2 October 1997

We study the dynamics of a system composed of interacting units each with a complex internal structure comprising many subunits and treat the case in which each subunit grows in a multiplicative manner. We propose a model for such systems in which the interaction among the units is treated in a mean field approximation and the interaction among subunits is nonlinear. We test the model and find agreement between our predictions and empirical results based on a large economics database spanning 20 years.


©1998 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevLett.80.1385
DOI: 10.1103/PhysRevLett.80.1385
PACS: 05.40.+j, 05.70.Ln, 64.60.Lx, 87.10.+e

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