Non-linear space-time behaviour of space-dependent stochastic center manifold in power-reactor dynamics

The dynamical behavior of nuclear power reactors near the onset of a power-oscillation is studied in conjunction with a stochastic nonlinear center manifold equation. Geometrical relations are given to identify nonlinear terms from time-series data with the use of the probability distribution function for the center manifold equation and/or to seek an expedient indicator of reactor stability which will be replaced by the damping ratio. The irreversible circulation of fluctuation is discussed as an example. A nonlinear space-dependent stochastic center manifold is also presented. Nonlinear features in connection with neutron fluctuations are discussed which have been observed in practical nuclear reactors, e.g., the critical fluctuation, and the phase turbulence. (author)