This article is devoted to the results of phase topology research on a generalized mathematical model, which covers such two problems as the dynamics of two point vortices enclosed in a harmonic trap in a Bose – Einstein condensate and the dynamics of two point vortices bounded by a circular region in an ideal fluid. New bifurcation diagrams are obtained and three-into-one and four-into-one tori bifurcations are observed for some values of the physical parameters of the model. The presence of such bifurcations in the integrable model of vortex dynamics with positive intensities indicates a complex transition and a connection between bifurcation diagrams in both limiting cases. In this paper, we analytically derive equations that define the parametric family of bifurcation diagrams of the generalized model, including bifurcation diagrams of the specified limiting cases. The dynamics of the bifurcation diagram in a general case is shown using its implicit parameterization. A stable bifurcation diagram, related to the problem of dynamics of two vortices bounded by a circular region in an ideal fluid, is observed for particular parameters’ values.

中文翻译：

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一类广义涡旋积分模型的分叉图

本文致力于在广义数学模型上进行相拓扑研究的结果，该模型涵盖了两个问题，例如，玻色-爱因斯坦凝聚物中谐波陷阱中封闭的两点涡旋的动力学以及由aose约束的两点涡旋的动力学。理想流体中的圆形区域。获得了新的分叉图，并对模型的物理参数的某些值观察到三合一和四合一的托里分叉。在具有正强度的涡旋动力学的可积模型中，这种分叉的存在表明在两种极限情况下，复杂的过渡和分叉图之间的联系。在本文中，我们通过分析得出定义广义模型分叉图参数族的方程，包括指定极限情况的分叉图。一般情况下，使用其隐式参数化显示了分叉图的动态。对于特定参数的值，观察到一个稳定的分叉图，该图与理想流体中以圆形区域为边界的两个涡流的动力学问题有关。