摘要：In this paper, the development of our previously proposed two-party electoral models, is proposed the nonlinear mathematical model with variable coefficients in the case of three-party elections, that describes the dynamics of the quantitative change of the votes of the pro-government and two opposition parties from election to election. The model considers four objects: state and administrative structures, acting by means of administrative resources for opposition-minded voters with the aim to win their support for the pro-government party; voters who support the first opposition party; voters who support the second opposition party; voters who support the pro-government party. The model takes into account the change in the total number of voters in the period from election to election, i.e. the so-called demographic factor during the elections is taken into account. We have considered two cases: when the elections are held without falsification and when there are cases of falsification by the Election Commission in favor of the pro-government party. The model considered the cases with variable coefficients. In particular, we assume that in the period between elections coefficients of "attracting" voters are exponentially increasing function of time. In the particular case we obtain exact analytical solutions. The conditions have been identified under which the opposition can win the forthcoming elections, and in some cases, the pro-government party can stay in power. In general Cauchy problem was solved numerically using the MATLAB software package. We get different variations of the outcome of the election based on voter turnout, the possible falsification of elections and demographic factors. The proposed mathematical and computer model has both theoretical and practical importance. Political opponents (the power and opposition parties) can use our results: to choose a strategy, to calculate its abilities (selecting parameters) in order to achieve the set goal.
关键词：nonlinear model of elections; pro-government party; the oppositions parties ; falsification; voter turnout; demographic factor
