Dynamical behaviour of a large complex system

Jianfeng Feng; Mariya Shcherbina; Brunello Tirozzi

doi:10.3934/cpaa.2008.7.249

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2008, Volume 7, Issue 2: 249-265. Doi: 10.3934/cpaa.2008.7.249

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Dynamical behaviour of a large complex system

1.
Department of Computer Science and Mathematics, Warwick University, Coventry CV4 7AL
2.
Institute for Low Temperature Physics, Lenin ave 47, 61103
3.
Department of Physics, Rome Univ. "La Sapienza", P. Aldo Moro 5, 00185 Roma

Received: December 31, 2006

Revised: May 31, 2007

Published: February 2008

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Abstract

Limit theorems for a linear dynamical system with random interactions are established. The theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is weakly stable or unstable (see Definition 1 below).

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Mathematics Subject Classification: Primary: 60-xx, 93-xx; Secondary: 93Dxx.

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