Geodesic
On the uniqueness of a positive stationary state in the dynamics of a population with asymmetric competition
Informatics and Automation, Optimal control, Tome 291 (2015), pp. 86-94.

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

For a nonlinear model of the dynamics of a size-structured (exploited) population with asymmetric form of competition, we prove a uniqueness theorem for a positive stationary solution under sufficiently general assumptions on the parameters of the model. 
@article{TRSPY_2015_291_a7,
     author = {A. A. Davydov and A. F. Nassar},
     title = {On the uniqueness of a positive stationary state in the dynamics of a population with asymmetric competition},
     journal = {Informatics and Automation},
     pages = {86--94},
     publisher = {mathdoc},
     volume = {291},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a7/}
}
TY  - JOUR
AU  - A. A. Davydov
AU  - A. F. Nassar
TI  - On the uniqueness of a positive stationary state in the dynamics of a population with asymmetric competition
JO  - Informatics and Automation
PY  - 2015
SP  - 86
EP  - 94
VL  - 291
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a7/
LA  - ru
ID  - TRSPY_2015_291_a7
ER  - 
%0 Journal Article
%A A. A. Davydov
%A A. F. Nassar
%T On the uniqueness of a positive stationary state in the dynamics of a population with asymmetric competition
%J Informatics and Automation
%D 2015
%P 86-94
%V 291
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a7/
%G ru
%F TRSPY_2015_291_a7
A. A. Davydov; A. F. Nassar. On the uniqueness of a positive stationary state in the dynamics of a population with asymmetric competition. Informatics and Automation, Optimal control, Tome 291 (2015), pp. 86-94. http://geodesic.mathdoc.fr/item/TRSPY_2015_291_a7/

[1] Arnold V.I., “Zhestkie” i “myagkie” matematicheskie modeli, MTsNMO, M., 2000

[2] Davydov A.A., Nassar A.F., “O statsionarnom sostoyanii v dinamike populyatsii s ierarkhicheskoi konkurentsiei”, UMN, 69:6 (2014), 179–180 | DOI | MR | Zbl

[3] Davydov A.A., Nassar A.F., “Stationary regime of exploitation of size-structured population with hierarchical competition”, J. Math. Sci., 205:2 (2015), 199–204 | DOI | Zbl

[4] Davydov A.A., Platov A.S., “Optimal stationary solution in forest management model by accounting intra-species competition”, Moscow Math. J., 12:2 (2012), 269–273 | MR | Zbl

[5] Davydov A.A., Platov A.S., “Optimalnoe statsionarnoe reshenie modeli ekspluatatsii populyatsii pri uchete vnutrividovoi konkurentsii”, Sovr. matematika. Fund. napr., 46 (2012), 44–48

[6] Von Foerster H., “Some remarks on changing populations”, The kinetics of cellular proliferation, Ed. by F. Stohlman, Grune Stratton, New York, 1959, 382–407

[7] Hritonenko N., Yatsenko Yu., Goetz R.-U., Xabadia A., “Optimal harvesting in forestry: Steady-state analysis and climate change impact”, J. Biol. Dyn., 7:1 (2013), 41–58 | DOI | MR

[8] Koddington E.A., Levinson N., Teoriya obyknovennykh differentsialnykh uravnenii, LKI, M., 2007

[9] Maltus T.R., Opyt o zakone narodonaseleniya, ili izlozhenie proshedshego i nastoyaschego deistviya etogo zakona na blagodenstvie chelovecheskogo roda, s prilozheniem neskolkikh issledovanii o nadezhde na otstranenie ili smyagchenie prichinyaemogo im zla, T. 1, 2, Tip. I.I. Glazunova, SPb., 1868

[10] McKendrick A.G., “Applications of mathematics to medical problems”, Proc. Edinburgh Math. Soc., 44 (1926), 98–130 | DOI

[11] Murphy L.F., “A nonlinear growth mechanism in size structured population dynamics”, J. Theor. Biol., 104:4 (1983), 493–506 | DOI

[12] Panesh A.A., Platov A.S., “Optimization of size-structured population with interacting species”, J. Math. Sci., 188:3 (2013), 293–298 | DOI | MR | Zbl

[13] Rudin U., Osnovy matematicheskogo analiza, Mir, M., 1976

[14] Structured-population models in marine, terrestrial, and freshwater systems, Ed. by S. Tuljapurkar, H. Caswell, Chapman Hall, New York, 1997

[15] Verhulst P.-F., “Notice sur la loi que la population suit dans son accroissement”, Correspondance math. phys., 10 (1838), 113–121