FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 4, PAGES 1035-1045

**Problems and theorems of variational modeling in ecology of
communities**

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