Geodesic
Mathematical aspects of variation modelling in ecology of communities
Matematičeskoe modelirovanie, Tome 6 (1994) no. 5, pp. 55-76.

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

Variation problem is examined which arises as the result of the extremal principles application in the ecology of the communities. The theorems of existence and uniqueness of the variation problem solutions are proved, the properties of invariant extremals to transformations of the parameters problem are investigated. Theorem of the stratification is proved: the space of the parameters of problem $R_+^m=\{\vec L\in R^m, L^1>0,L^2>0,\dots,L^m>0\}$ divides on $2^m-I$ nonintersecting subsets $S^J$; in each of them the extremal problem with restrictions – inequalities is equal to problem with restrictions – equalities for certain unempty part $J\subset\{1,2,\dots,m\}$ of the starting parameters of problem. Biological interpretation of these theorems and results of the numerical investigation of the concrete communities are adduced. 
@article{MM_1994_6_5_a4,
     author = {A. P. Levich and V. L. Alekseev and V. A. Nikulin},
     title = {Mathematical aspects of variation modelling in ecology of communities},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {55--76},
     publisher = {mathdoc},
     volume = {6},
     number = {5},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1994_6_5_a4/}
}
TY  - JOUR
AU  - A. P. Levich
AU  - V. L. Alekseev
AU  - V. A. Nikulin
TI  - Mathematical aspects of variation modelling in ecology of communities
JO  - Matematičeskoe modelirovanie
PY  - 1994
SP  - 55
EP  - 76
VL  - 6
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_1994_6_5_a4/
LA  - ru
ID  - MM_1994_6_5_a4
ER  - 
%0 Journal Article
%A A. P. Levich
%A V. L. Alekseev
%A V. A. Nikulin
%T Mathematical aspects of variation modelling in ecology of communities
%J Matematičeskoe modelirovanie
%D 1994
%P 55-76
%V 6
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_1994_6_5_a4/
%G ru
%F MM_1994_6_5_a4
A. P. Levich; V. L. Alekseev; V. A. Nikulin. Mathematical aspects of variation modelling in ecology of communities. Matematičeskoe modelirovanie, Tome 6 (1994) no. 5, pp. 55-76. http://geodesic.mathdoc.fr/item/MM_1994_6_5_a4/