Geodesic
The mathematical model of the number dynamic for the homogeneous exploited population and analysis of the trade influence on the dynamic character
Dalʹnevostočnyj matematičeskij žurnal, Tome 3 (2002) no. 1, pp. 108-122.

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

In this work were analyzed the contradictions between the strategy of the optimum withdrawal and population stability. As an example we have used the homogeneous population with periodical reproduction (the mathematical model with discrete time). The annual withdrawal was formalized through the exploitation intensity (trade effort amount) depending on the of the exploited population level. The optimum strategy of the withdrawal is intended to achieve the maximal yield while preserving the stable population level. We have shown, that the equilibrium population stock remains stable when exploitation intensity is constant and can become unstable at variable intensity. Thus, it was shown that the exploitation with the variable ratio of withdrawal can cause the fluctuation of population stock, or force transition of the population to the new stationary level, which frequently means the degeneration of the population. 
@article{DVMG_2002_3_1_a11,
     author = {E. Ya. Frisman and E. V. Sycheva and Yu. G. Izrailsky},
     title = {The mathematical model of the number dynamic for the homogeneous exploited population and analysis of the trade influence on the dynamic character},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {108--122},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2002_3_1_a11/}
}
TY  - JOUR
AU  - E. Ya. Frisman
AU  - E. V. Sycheva
AU  - Yu. G. Izrailsky
TI  - The mathematical model of the number dynamic for the homogeneous exploited population and analysis of the trade influence on the dynamic character
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2002
SP  - 108
EP  - 122
VL  - 3
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2002_3_1_a11/
LA  - ru
ID  - DVMG_2002_3_1_a11
ER  - 
%0 Journal Article
%A E. Ya. Frisman
%A E. V. Sycheva
%A Yu. G. Izrailsky
%T The mathematical model of the number dynamic for the homogeneous exploited population and analysis of the trade influence on the dynamic character
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2002
%P 108-122
%V 3
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2002_3_1_a11/
%G ru
%F DVMG_2002_3_1_a11
E. Ya. Frisman; E. V. Sycheva; Yu. G. Izrailsky. The mathematical model of the number dynamic for the homogeneous exploited population and analysis of the trade influence on the dynamic character. Dalʹnevostočnyj matematičeskij žurnal, Tome 3 (2002) no. 1, pp. 108-122. http://geodesic.mathdoc.fr/item/DVMG_2002_3_1_a11/

[1] S. Buckland, S. Ahmadi, B. W. Staines, I. J. Gordon, and R. W. Youngson, “Estimating the minimum population size that allows a given annual number of mature red stags to be culled sustainably”, J. of App. Ecol., 33 (1997), 118–130 | DOI

[2] M. B. Schaefer, “Some aspects of the dynamics of population important to the management of the commercial marine fisheries”, Bull. Inter-Am. Trop. Tuna Comm., 2:1 (1954), 27–56

[3] A. I. Abakumov, Upravlenie i optimizatsiya v modelyakh ekspluatiruemykh populyatsii, Dalnauka, Vladivostok, 1993, 129 pp.

[4] R. Biverton, S. Kholt, Dinamika chislennosti promyslovykh ryb, Pischevaya promyshlennost, M., 1969, 248 pp.

[5] U. E. Riker, Metody otsenki i interpretatsiya biologicheskikh pokazatelei populyatsii ryb, Pischevaya promyshlennost, M., 1979, 408 pp.

[6] I. E. Lokshina, Dinamika promysla i otsenka vylova, Pisch. prom-st, M., 1978, 68 pp.

[7] B. V. Tyurnin, “K voprosu o zapasakh okhotskoi seldi”, Izvestiya TINRO, 59 (1965), 71–81

[8] V. P. Shuntov, Biologicheskie resursy Okhotskogo morya, Agropromizdat, M., 1985, 224 pp.