摘要：In the real model it is supposed that the powerful state with a widespread state language carries out assimilation of the population of less powerful state and the third population talking in two languages, different in prevalence. Carries out assimilation of the population of the state formation with the least widespread language to the turn, less powerful state.Not triviality of model assumes negative demographic factor of the powerful state-assimilating and positive demographic factor of the state formation which is under bilateral assimilation. For some ratios between demographic factors of the sides and coefficients of assimilations, for nonlinear system of three differential equations with the corresponding conditions of Cauchy the first integrals are found.In particular, in the first case the first integral in space of required functions represents a hyperbolic paraboloid, and in the second case – a cone. In these cases, the nonlinear system of three differential equations is reduced to nonlinear system of two differential equations for which the second first integrals are found and in the phase plane of decisions are investigated behavior of integrated curves.In more general case with application of a criteria of Bendikson the possibility of existence of the closed integrated curves is proved that indicates a possibility of a survival of the population finding under double assimilation.
