### Mathematical Modelling of Aquatic Ecosystem

#### Abstract

In present paper we consider the complete statements of initial-boundary problems for the modelling of various aspects of aqueous systems in Latvia. All the proposed models are the evolutionary models: all they are nonstationary and continuous qualitative models having the dynamic parameters and aimed at analysis, evaluation and forecast of aqueous systems (reservoirs, lakes and seas). In constructing these mathematical models as research tools classic apparatus of differential equations (both ODE and PDE) as well as apparatus of mathematical physics were used.

#### Keywords

#### Full Text:

PDF#### References

G. I. Marchuk, Mathematical modelling in environmental problem. Moscow: Science, 1982.

J. Jennifers, Introduction to system analysis: application for ecology. Moscow: World, 1981.

Yu. P. Zaitsev, and G. G. Polikarpov, "Ecological processes in the critical areas of the Black Sea: synthesis of the results of two research dimensions from the middle of the XX to the beginning of XXI centuries." Marine Ecological Journal, Vol. 1, Issue 1, pp. 33-55. 2002.

J. Hofbauer, and K. Sigmund, The theory of Evolution and dynamical systems. London: Cambridge University Press, 1988.

L. M. Nedostup, "Sensitivity of the water ecosystem models that are affected by the anthropogenic factor." in Natural waters preservation, protection and quality improvement problems. Moscow: Science, 1982, pp. 139-155.

B. Bolin, "Model studies of the Baltic Sea." University of Stockholm, Institute of Meteorology, Ambio Special Report (Report GH-4), No. 1, 1972. pp. 115-119.

S. Sjoberg, "A mathematical and conceptual framework for models of the pelagic ecosystems of the Baltic Sea." University of Stockholm, Asko Laboratory, Report No. 1, 1980. 206 p.

Yu. M. Barabasheva, L. I. Brodsky, and G. I. Devyatkova, "About evaluation of parameters in the point model of aquatic ecosystem: Theoretical ecology." Moscow: Lomonosov Moscow State University publishing, 1987, pp. 105-110.

Sh. E.Guseynov, E. A. Kopytov, and O. V. Schiptsov, Mathematical Models of an exhaust concentration dynamics in urban atmosphere. Riga: Transport and Telecommunication Institute Press, 2010.

J. S.Rimshans, I. N. Esau, S. S. Zilitenkevich, and Sh. E. Guseynov, "Analytical-Numerical Solution for the One Dimensional PBL Turbulence Model." Proceedings of the 18th Symposium on Boundary Layers and Turbulence under the aegis of the American Meteorological Society, Stockholm, Sweden June 09-13, 2008. http://ams.confex.com/ams/pdfpapers/139877.pdf.

Yu. N. Sergeyev, "Problem of mathematical modeling of multicomponent physico-biological marine system." Herald of the Leningrad State University, Issue: 24, pp. 114-125, 1972.

S. Sjoberg, F. Wulff and P. Wahllstrom, "Computer Simulations of Hydrochemical and Biological processes in the Baltic." University of Stockholm, Asko Laboratory, Report No 1, 1972. 180 p.

L. F. Serdiutskaya, "Study of mathematical models of environmental systems using multivariate factor analysis." International Journal on Engineering Simulation, Vol. 17, pp. 417-428, 2000.

L. F. Serdyutskaya, "About some aspects of factorial analysis application for the problems of environmental simulation." in Modelling and diagnostics of the sophisticated processes and systems, Kiev: Scientific thaught, 1997, pp. 35-40.

V. I. Belyaev, Ye. D. Korenyuk, and V. K. Hrusch, Computer modelling of the subsurface water circulation and pollution dynamics. Dnepropetrovsk: Science and Education, 2001.

2010 Environmental Performance Index. Yale Center for Environmental Law & Policy, 2010, 87 p.

HELCOM Initial Holistic Assessment. Ecosystem Health of the Baltic Sea in 2003-2007. Baltic Sea Environment Proceedings, No. 122, 2008, 66 p.

Latvian Ministry of Environment. Environmental Policy Strategy in 2009–2015. Informative section. Riga, 2009, 53 p.

Sh. E.Guseynov, J. S. Rimshans, and E. A. Kopytov, "Solution of the Model of Exhaust Concentration Dynamics in Urban Atmosphere under Unknown Turbulent Air Flow Velocity." International Journal of Procedia Environmental Sciences, Series: Urban Environmental Pollution, 2011, No 4, pp. 35-42, 2011.

S. I. Kuznetsov, Micro flora of the lakes and its geochemical activity. Moscow: Science, 1970.

W. Eppley, E. U. Renger, and E. L. Uenrick, "A study of plankton dynamics and nutrient cycling in the central gyre of the North Pacific Ocean." Journal on Limnology and Oceanography, Vol. 18, Issue 4, pp. 534-555, 1973.

Baltic Marine Environment Protection Commission: Helsinki Commission. Baltic Sea Environment Proceedings, No. 16, 1986, 176 p.

Baltic Marine Environment Protection Commission: Helsinki Commission. First Periodic assessment of the State of the Marine Environment of the Baltic Sea area, General Conclusions. Baltic Sea Environment Proceedings, No. 17A, 1986, 56 p.

V. B. Georgievsky, "Identification and verification of the water ecosystem models." in Natural waters preservation, protection and quality improvement problems. Moscow: Science, 1982, pp. 156-163.

V. B. Georgievsky, "Identification and mathematical modeling of the eutrophication processes of the sea ecosystems." Ambio Special Report, Vol. 5, pp. 165-176, 1983.

J.Hofbauer, and K. Sigmund, The theory of Evolution and dynamical systems. London: Cambridge University Press, 1988.

V. I. Arnold, Additional chapters of the ordinary differential equations theory. Moscow: Science, 1978.

V. A. Yakubovich, and V. M. Starshinsky, Linear differential equations with periodic coefficients and their applications. Moscow: Science, 1972.

DOI: https://doi.org/10.17770/etr2015vol3.192

### Refbacks

- There are currently no refbacks.