A Model Studying the Relationship between Lake Water Salinity and Water Level Fluctuations

Czyżycki, Tomasz; Dzhalladova, Irada; Růžičková, Miroslava

doi:10.2478/tmmp-2025-0027

Abstract

We study a model represented by a system of ordinary differential equations describing fluctuations in the level of a saltwater lake, for example the Caspian Sea, depending on its salinity. The search for an analytical solution using the Laplace transform is discussed, and a numerical method for finding a variety of solutions in the neighborhood of the singular point of the studied model is also shown. The properties of the solutions obtained by simulation for some values of the coefficients of the studied system are discussed. This dependence is also demonstrated by numerically constructed solutions in the neighborhood the singular point of the studied model.

References

ASCHER, W.—MIROVITSKAYA, N.: The Caspian Sea: A Quest for Environmental Security. Proceedings of the NATO Advanced Research Workshop on The Caspian Sea, Kluwer Academic Publishers, Dordrecht, Boston, London, 1999.
Search in Google Scholar Back to article
IBRAYEV, R. A.—ÖZSOY, E.—SCHRUM, C.—SUR, H. I.: Seasonal variability of the Caspian Sea three-dimensional circulation, sea level and air-sea interaction, Ocean Sci. 6 (2010), 311–329.
Search in Google Scholar Back to article
KOSTIANOY, A. G.—KOSAREV, A. N.: The Caspian Sea Environment. Springer--Verlag, Berlin, 2005.
Search in Google Scholar Back to article
ZONN, I. S.—KOSTIANOY, A. G.—KOSAREV, A. N.—GLANTZ, M. H.: The Caspian Sea Encyclopedia. Springer-Verlag, Berlin, 2010.
Search in Google Scholar Back to article
KRANTZ, S. G.: Handbook of Complex Variables. Birkh¨auser Boston MA, Springer Science & Business Media, New York, 1999. https://doi.org/10.1007/978-1-4612-1588-2
Search in Google Scholar Back to article
GIKHMAN, I. I.—SKOROKHOD, A. V.: Controlled Stochastic Processes. Springer--Verlag, Berlin, 1979.
Search in Google Scholar Back to article
DZHALLADOVA, I. A.: Optimization of Stochastic System. KNEU, Kiev, 2005. (In Ukrainian)
Search in Google Scholar Back to article
DIBĹIK, J.—DZHALLADOVA, I. A.—RŮŽIČKOVÁ, M.: Stabilization of company’s income modeled by a system of discrete stochastic equations, Adv. Difference Equ. 2014, 2014:289, 8 pp.
Search in Google Scholar Back to article
DIBĹIK, J.—DZHALLADOVA, I. A.—MICHALKOVÁ, M.— RŮUŽIČKOVÁ, M.: Moment equations in modeling a stable foreign currency exchange market in conditions of uncertainty, Abstr. Appl. Anal. 2013 (2013), Art. ID 172847, 11 pp.
Search in Google Scholar Back to article
DZHALLADOVA, I. A.—RŮŽIČKOVÁ, M.: Dynamical systems with random structure and its applications. Stability, Oscillations and Optimization of Systems Vol. 10, Cambridge Scientific Publishers, Cambridge, 2020.
Search in Google Scholar Back to article

A Model Studying the Relationship between Lake Water Salinity and Water Level Fluctuations

Abstract

Paradigm

My account