FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2002, VOLUME 8, NUMBER 4, PAGES 1035-1045
A. P. Levich
P. V. Fursova
Abstract
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The formulations of variation problem of ecological
community, the existence and uniqueness theorems of the
variation problem solutions and the stratification theorem are given in
this article. For ecological application ``the Gibb's theorem''
is proved --- it is an analogue of equivalence of maximum entropy
with fixed energy level problem and minimum energy with fixed
entropy level problem. Monotone increasing property of extended
entropy functional is formulated and proved. In the case, when the
number of limiting resources is greater than the number of species,
balance equations are sufficient for finding the population size. The
compatibility condition for the corresponding system is found. The
property of variation problem for ``close'' species, i. e.
species with ``almost'' proportional quotas are described.
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Last modified: April 10, 2003