Geodesic
Problems and theorems of variational modeling in ecology of communities
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 4, pp. 1035-1045

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{FPM_2002_8_4_a6,
     author = {A. P. Levich and P. V. Fursova},
     title = {Problems and theorems of variational modeling in ecology of communities},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1035--1045},
     publisher = {mathdoc},
     volume = {8},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2002_8_4_a6/}
}
TY  - JOUR
AU  - A. P. Levich
AU  - P. V. Fursova
TI  - Problems and theorems of variational modeling in ecology of communities
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2002
SP  - 1035
EP  - 1045
VL  - 8
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2002_8_4_a6/
LA  - ru
ID  - FPM_2002_8_4_a6
ER  - 
%0 Journal Article
%A A. P. Levich
%A P. V. Fursova
%T Problems and theorems of variational modeling in ecology of communities
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2002
%P 1035-1045
%V 8
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2002_8_4_a6/
%G ru
%F FPM_2002_8_4_a6
A. P. Levich; P. V. Fursova. Problems and theorems of variational modeling in ecology of communities. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 4, pp. 1035-1045. http://geodesic.mathdoc.fr/item/FPM_2002_8_4_a6/