A model studying the relationship between lake water salinity and water level fluctuations

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.
Such dependence is also demonstrated by numerically constructed solutions in the neighborhood the singular point of the studied model.