Dynamics of population kinetics model with cosymmetry
Matematičeskoe modelirovanie, Tome 20 (2008) no. 2, pp. 85-92.

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

Dynamics of a cosymmetric system of nonlinear parabolic equations is studied to model population kinetics of three interacting species. Finite-difference scheme which preserves a cosymmetry of the underlying problem is developed. Method of computation for continuous family of equilibria is derived. Different scenarios of instability in the model are analyzed as well as evolution of nonstationary regimes and families of steady states.
@article{MM_2008_20_2_a7,
     author = {E. S. Kovaleva and V. G. Tsybulin and K. Frischmuth},
     title = {Dynamics of population kinetics model with cosymmetry},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {85--92},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_2_a7/}
}
TY  - JOUR
AU  - E. S. Kovaleva
AU  - V. G. Tsybulin
AU  - K. Frischmuth
TI  - Dynamics of population kinetics model with cosymmetry
JO  - Matematičeskoe modelirovanie
PY  - 2008
SP  - 85
EP  - 92
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2008_20_2_a7/
LA  - ru
ID  - MM_2008_20_2_a7
ER  - 
%0 Journal Article
%A E. S. Kovaleva
%A V. G. Tsybulin
%A K. Frischmuth
%T Dynamics of population kinetics model with cosymmetry
%J Matematičeskoe modelirovanie
%D 2008
%P 85-92
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2008_20_2_a7/
%G ru
%F MM_2008_20_2_a7
E. S. Kovaleva; V. G. Tsybulin; K. Frischmuth. Dynamics of population kinetics model with cosymmetry. Matematičeskoe modelirovanie, Tome 20 (2008) no. 2, pp. 85-92. http://geodesic.mathdoc.fr/item/MM_2008_20_2_a7/

[1] Murray J. D., Mathematical biology, Springer, New York, 1993, 766 pp. | MR

[2] Yudovich V. I., “Kosimmetriya, vyrozhdenie reshenii operatornykh uravnenii, vozniknovenie filtratsionnoi konvektsii”, Matem. zametki, 49:5 (1991), 142–148 | MR | Zbl

[3] Yudovich V. I., “Secondary cycle of equilibria in a system with cosymmetry, its creation by bifurcation and impossibility of symmetric treatment of it”, Chaos, 5:2 (1995), 402–411 | DOI | MR | Zbl

[4] Kurakin L. G., Yudovich V. I., “Bifurkatsii pri monotonnoi potere ustoichivosti ravnovesiya kosimmetrichnoi dinamicheskoi sistemy”, DAN, 372:1 (2000), 29–33 | MR | Zbl

[5] Govorukhin V. N., “Calculation of one-parameter families of stationary regimes in a cosymmetric case and analysis of plane filtrational convection problem”, Continuation methods in fluid dynamics (Aussois, 1998), Notes Numer. Fluid Mech., 74, Vieweg, Braunschweig, 2000, 133–144 | MR | Zbl

[6] Frischmuth K., Tsybulin V. G., “Families of equilibria and dynamics in a population kinetics model with cosymmetry”, Physics Letters A, 338 (2005), 51–59 | DOI | Zbl

[7] Frischmuth K., Tsybulin V. G., “Computation of a family of non-cosymmetrical equilibria in a system of two nonlinear parabolic equations”, Computing, 16, Suppl. (2002), 67–82 | MR

[8] Kantur O. Yu., Tsibulin V. G., “Spektralno-raznostnyi metod rascheta konvektivnykh dvizhenii zhidkosti v poristoi srede i sokhranenie kosimmetrii”, Zh. vychisl. matem. i matem. fiz., 42:6 (2002), 913–923 | MR | Zbl