Analysis Based on Moment Vector Equation for Interacting Identical Elements with Nonlinear Dynamics

Hideki SATOH  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A   No.10   pp.1765-1774
Publication Date: 2010/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.1765
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
MVE,  nonlinear,  many-body,  eigen analysis,  

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A method was developed for analyzing a system comprised of identical and indistinguishable elements with nonlinear dynamics. First, a moment vector equation (MVE) for the system was derived so as to avoid the curse of dimensionality by using the property that the elements are identical and indistinguishable. Next, an algorithm was developed to solve the MVE for deriving the moment vector in a steady state. It effectively uses eigen analysis on the basis of the property of the MVE. It can thus be used to clarify the structure of the solutions in the moment vector space and to derive multiple solutions by setting the initial value to the moment vector orthogonal to the solutions already obtained. Finally, the probability density function (pdf) for the state of the system was derived using the moment vectors in a steady state. Comparison of the pdfs thereby derived with those derived using numerical simulation showed that the method provided good approximations of the pdfs. Moreover, multiple solutions that are difficult to do using numerical simulation were derived.