Yeast cells S. pombe are examples of biological organisms in which the mixing of genetic material during meiosis occurs due to oscillation of the nucleus. Such oscillations were observed experimentally and in previous research developed a theoretical model that describes the mechanisms that drive the oscillation. In this paper we found numerical solutions for the theoretical model, conducted the analysis of linear stability and examined the occurrence of Hopf bifurcation in the space of parameters whose values are not known from experiments: k_on c i f_c. This resulted in the bifurcation diagram in which the values of the parameters identified areas in which the model as solutions provide stable and unstable periodic orbits. It was found that for the value of the parameter fc > 5:8pN system will never show oscillatory behavior, while for f_c less or quivalent 1:75pN reported the occurrence of subcritical Hopf bifurcation. Within the interval 1:75pN less or quivalent f_c < 5:8pN changing parameter k_on c from zero to greater values, system will quickly develop a stable oscillations.