Hopf Bifurcation In A Model Of Nuclear Reactor With Heat-transfer Delay

As an efficient and environment-friendly energy, nuclear power can dramatically reduce air pollution and promote energy independence of our country. The development of nuclear power industry cannot be separated from the issue of nuclear security. In protecting the security of the reactor core in the process of nuclear reaction, nuclear power control system plays an irreplaceable role. The system mainly makes sure the normal operation of nuclear power station by measuring the average temperature of the coolant and controll ing the reactor capability. Therefore, temperature and power are two critical variables in researching operation security of nuclear reactor.This paper carries out a dynamic properties analysis of two-dimensional nuclear reactor model with time delay which was established by Kostas Bucys. Here the delay, the time require for coolant through the pipe line, describes the measurement of temperature in the reactor of nuclear power plant control system. This paper studies the stability of two equilibria bases on parametert, and then we obtain the sufficient conditions of the existence of local Hopf bifurcations. The direction of Hopf bifurcation and the stability of periodic solutions bifurcating at positive fixed point are researched in this paper and the explicit formula is derived, bases on the center manifold theorem and normal form method established by Hassard. Then, basing on the global Hopf bifurcation theory proposed by Wu, the research is shifted to the global existence of periodic solution. Based on the above theorem, we obtain the effect of delayt, the time required for the coolant pipe, on the safety of the reactor core. When the delay is controlled in a certain range, and the parameters in the model satisfy certain conditions, both temperature and power of the reactor will be limited within a range. Finally, we conduct numerical simulation by use of MATLAB software and illustrate the theoretical results. Numerical simulation also shows that when the parameters satisfy certain conditions, reactor power and temperature will not rise to unacceptable levels.