ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Last E. V., Sycheva E. V., Frisman E. Y. Influence of a nonlinear trade on natural populations’ dynamics. Izvestiya VUZ. Applied Nonlinear Dynamics, 2003, vol. 11, iss. 4, pp. 89-105. DOI: 10.18500/0869-6632-2003-11-4-89-105

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Language: 
Russian
Heading: 
Nonlinear Dynamics in Action
Article type: 
Article
UDC: 
574.3
DOI: 
10.18500/0869-6632-2003-11-4-89-105

Influence of a nonlinear trade on natural populations’ dynamics

Autors: 
Last Elena Valerevna, Institute of Automation and Control Processes, FEB RAS (IASP FEB RAS)
Sycheva Ellina Vladimirovna, Institute of Automation and Control Processes, FEB RAS (IASP FEB RAS)
Frisman Efim Yakovlevich, Institute for Complex Analysis of Regional Problems of Russian Academy of Sciences, Far Eastern Branch
Abstract: 

This work is devoted to construction and research of mathematical model of number dynamics of biological populations subjected to seasonal trade. The special attention is given to formalization оf dependence the catch size from present number оf а population and trading characteristics, and also to analysis of contradictions between aspiration ог maximum profit аnd stability оf population dynamics. Simulation data are compared with fishery statistics for some concrete species of fishes and invertebrates.

Key words: 
-
Acknowledgments: 
This work was supported by the Russian Foundation for Basic Research, grants. № 99-01-00633, 03-01-00044.
Reference: 
  1. Rusanov YS. Hunting and Fauna Conservation: The Impact of Hunting on the Structure of Populations Of Hunting Areas. Moscow: Lesnaya Promyshlennost; 1973. 145 p. (in Russian).
  2. Formozov AN. Fluctuations in the Number of Game Animals. Moscow; Leningrad: Koiz; 1935. 103 p. (in Russian).
  3. Kiris ID. Squirrel. Kirov: Volgo-Vyatka Book Publishing House. Kirov Branch; 1973. 448 p. (in Russian).
  4. Ashikmina EV, Frisman EY, Skaletskaya ЕI., Kulikov АN. Mathematical model for dynamics оf the number оf pelf products from the local population оf Manchurian squirrels. Ecological Modelling. 1985;30:145-156.
  5. Beverton RJH, Holt SJ. On the Dynamics of Exploited Fish Populations. Dordrecht: Springer; 1993. 538 p. DOI: 10.1007/978-94-011-2106-4.
  6. Richer WE. Stock and recruitment. Th. J. Fisheries Res. Bard. Саn. 1954;11(5):559-623. DOI: 10.1139/f54-039.
  7. Ricker WE. Computation and Interpretation of Biological Statistics of Fish Populations. Ottawa: Bulletin of the Fisheries Research Board of Canada, Bulletin 191; 1975. 400 p.
  8. Gimelfarb AA, Ginzburg LR, Poluektov RA. Dynamic theory of biological populations. Moscow: Nauka; 1974. 455 p. (in Russian).
  9. Skaletskaya EI, Frisman EY, Shapiro AP. Discrete Models of Population Dynamics and Fisheries Optimization. Moscow: Nauka; 1979. 168 p. (in Russian).
  10. Abakumov AI. Management and Optimization in Models of Exploited Populations. Vladivostok: Dalnauka; 1993. 129 p. (in Russian).
  11. Shapiro AP. Mathematical models of competition. In: Management and Information. Vol. 10. Vladivostok: DVSC AS USSR; 1974. P. 5- 75 (in Russian).
  12. Shapiro AP, Luppov SP. Recurrence Equations in the Theory of Population Biology. Moscow: Nauka; 1983. 136 p. (in Russian).
  13. May RM. Simple mathematical models with very complicated dynamics. Nature. 1976;261(5560):459-467. DOI: 10.1038/261459a0.
  14. May RM. When two and two make four: nonlinear phenomena in ecology. Proc. В. Soc. London B. 1986;228(1252):241-266. DOI: 10.1098/rspb.1986.0054.
  15. Bazykin AD. Model of dynamics - numbers and - the problem of coexistence of closely related species. Journal of General Biology. 1969;30(3):259-264.
  16. Bazykin AD. Mathematical Biophysics - Interacting Populations. Moscow: Nauka; 1985. 181 p. (in Russian).
  17. Holling CS. The functional response оf predator to prey density and its role in mimicry and population regulation. Mem. Entomol. Soc. Canada. 1965;97(S45):5-60. DOI: 10.4039/entm9745fv.
  18. Schaefer MB. Some aspects of the dynamics of population important to the management оf the commercial marine fisheries. Bull. Inter-Am. Тгор. Tuna Comm. 1954;1(2):27.
  19. Lokshina IE. Fishery Dynamics and Catch Estimates. Moscow: Pichshevaya Promyshlennost; 1978. 66 p. (in Russian).
  20. Frisman EY, Sycheva EV, Izrailsky YG. Mathematical modeling of the population dynamics of homogeneous populations of commercial fish species. Far Eastern Mathematical Collection. 2002;3(1):108-122 (in Russian).
  21. Frisman E, Sycheva EV, Izrail'skii Y. Population dynamic instability of a commercial species induced by fishery. Doklady Biological Sciences. 2001;380(1-6):470-474. DOI: 10.1023/a:1012331623450.
  22. Bard Y. Nonlinear Parameter Estimation. Academic Press; 1974. 341 p.
  23. Greshilov AA, Stakun BA, Stakun AA. Mathematical Methods for Making Forecasts. Moscow: Radio I Svyaz; 1997. 112 p. (in Russian).
  24. Last EB, Frisman EY. The impact of fishing on the population dynamics of migratory fish species. Izvestiya VUZ. Applied Nonlinear Dynamics. 2002;10(1-2):157-169 (in Russian).
  25. Last EB, Luppov SP, Frisman EY. Dynamic instability in a mathematical model of population dynamics of salmon fish species. Far Eastern Mathematical Journal. 2001;2(1):114-125 (in Russian).
  26. Chigirinsky AI. Pacific salmon fishing in the Bering Sea. Ecology and Trophic Connections of Commercial Fish of the Far Eastern Seas: News of TINRO. 1994;116:142-151 (in Russian).
  27. Chigirinsky AI. Global natural factors, salmon fishing and numbers. Fisheries. 1993;(2):19-22 (in Russian).
  28. Kravchenko PZ. Discrete model of the dynamics of the number of age groups of female sockeye salmon. In: Mathematical Control in Population Biology. Vladivostok: Far Eastern Scientific Center of the USSR Academy of Sciences; 1985. P. 21 (in Russian).
  29. Sycheva EV. Characteristics of the fishery that determine the stability of the equilibrium size of the exploited population. In: Anniversary Collection of Scientific Works: To the 30th Anniversary of the Institute of Autonomous Agricultural Sciences FEB RAS. Vladivostok; 2001. P. 367 (in Russian).
Received: 
07.03.2003
Accepted: 
23.06.2003
Available online: 
30.11.2023
Published: 
31.12.2003
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