On the properties of solutions of some integro-differential problems of reactor dynamics

The conditions for completeness and summability of the root vectors in the spectral problem for the non-stationary system of the reactor kinetics integrodifferential equations in one-velocity approach with isotropic scattering have been determined. The results are generalized for energy dependence of cross sections. For nonlinear system describing reactor dynamics in a one-velocity kinetic approximation, taking into account delayed neutrons and dependence of cross sections on the medium temperature, existence of limit cycle (self-oscillations) is settled. In case of homogeneous medium and one-dimensional geometry it is proved that for investigated dynamical system the succession of bifurcations in the period-doubling is obeyed to the universal Feigenbaum's law