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Simple nonlinear recursions and the mean‐field concept
Author(s) -
Krause F.
Publication year - 1984
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.2113050602
Subject(s) - simple (philosophy) , nonlinear system , statistical physics , closure (psychology) , field (mathematics) , variety (cybernetics) , mean field theory , scheme (mathematics) , interval (graph theory) , random field , mathematics , physics , computer science , calculus (dental) , mathematical analysis , pure mathematics , statistics , quantum mechanics , combinatorics , epistemology , medicine , philosophy , dentistry , economics , market economy
Some questions concerning the formation of mean‐field theories are analyzed by a consideration of simple nonlinear recursions. The results suggest that a general closure scheme does not exist, rather there is a great variety of closures, each of the valid in only a certain interval of the characteristic parameter. Furthermore, questions connected with the appearance of random behaviour in these deterministic systems and the modelling of random reversals are discussed.