The research of a nuclear reactor model has been observed, where the system consists of two differential equations with one delay. A linear analysis has been performed, the asymptotic stability model of the area D0 and D2 has been defined, in which a stable periodic solution of one frequency appears. In the nonlinear analysis the analytical expression of the solution is presented with the help of bifurcation theories. In the numerical experiment using the scientific simulation program “Model Maker” numerical Runge–Kutta IV series method asymptotically stable solution and a stable periodic solution has been received and compared to the stable periodic solution received in nonlinear analysis with the help of bifurcation theories.