Abstract
In this paper we consider a completely Liouville integrable Hamiltonian system with two degrees of freedom, which describes the dynamics of two vortex filaments in a Bose-Einstein condensate enclosed in a harmonic trap. For vortex pairs of positive intensity detected bifurcation of three Liouville tori into one. Such bifurcation was found in the integrable case of Goryachev-Chaplygin-Sretensky in the dynamics of a rigid body. For the integrable perturbation of the physical parameter of the intensity ratio, identified bifurcation proved to be unstable, which led to bifurcations of the type of two tori into one and vice versa.
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