Non-linear dynamics of space-independent xenon oscillations

摘要

The space-independent xenon oscillation problem relevant to power nuclear reactors is studied. Xenon oscillations—both, without temperature feedback and in the presence of temperature feedback—have been analyzed semi-analytically and numerically. The effects of various parameters on the nature of bifurcation are studied. Bifurcation analysis shows that Hopf bifurcation occurs, and it is found that both sub-critical and super-critical Hopf bifurcation can occur in different regions of parameter space. Numerical experiments show that 'outside' the unstable periodic solutions that exist for the sub-critical Hopf bifurcation case, there exist large amplitude, stable periodic solutions to which the initial conditions, outside the basin of attraction of the stable fixed point, evolve. Though the existence of sub-critical Hopf bifurcation indicates that large amplitude perturbations even in the stable region may lead to initially diverging oscillations, it is reassuring that the oscillation amplitude remains bounded.