The expert complex of programs has been elaborated.It was applied for research of phenomenological parameters and related to them physical ones of the eclipsing variable binary stellar systems of different types – Algol (EA), ? Lyr (EB), W UMa (EW). It is shown that, unlike the generally accepted determination of «algols», as the systems with well noticeable beginning and end of eclipses, such eclipses can be registered also in the systems of type of EB and EW with relatively strong changes in parts of phase light curve out of eclipses. The contribution of eclipses is zero only for the elliptic systems that are sometimes erroneously classified as EW with small amplitude. The proposed method allows to specify such a classification, or to conduct the specified classification for new variable stars. We conducted the comparative analysis of dozens modifications of basic function, which describe the form of eclipses.These approximations were ranged in accordance to the quality of the approximations. As the main test function, the weighted sum of squares of deviations and the r.m.s. accuracy of approximation at the phases of observations was used. It is shown that the best results are shown byusing the approximations with functions, which are limited in a phase. Topological properties of the test functions are investigated in the multidimensional parameter space either for a phenomenological modeling, or, for a model with spherical components and homogeneous brightness. It is shown that the optimal algorithm of minimization is a combination of the «direct search» («brute force») for determination of the initial valued of the parameters, and further iterations using the method of differential corrections. For taking into account the limits of the parameter values, the possibility of automatic change of amount of parameters, which are corrected, is included. A phenomenological modeling better describes the light curves for the systems with the effects of «proximity» (ellipticity, reflection) and the O'Connell effect. Phenomenological parameters are used for a physical modeling of the two-color CCD observations of the new eclipsing variable system 2MASS J18024395 + 4003309 = VSX J180243.9 +400331, for that, taking into account the statistical dependences «mass – radius – luminosity», a self-consistent model is developed with a determination of radiuses, masses and temperatures of the components. The catalogue of phenomenological parameters of the new eclipsing variable binary systems is compiled. It contains the results of analysis of 65 runs of photometric observations of 58 systems, published in the «Open European Journal on Variable Stars», and contains both the parameters re-determined by us with best accuracy, and the additional introduced ones, which can be used for further theoretical modeling.
