Bifurcation of water column oscillator behavior analyzed by two-dimensional graphical method

A piecewise linear model which consists of the set of two linear ordinary differential equations with four parameters was derived to investigate the behavior of the water column oscillator simulating a safety system of an advanced reactor. The model shows various bifurcation. The behavior of the model can be discussed using the two-dimensional mapping function. When the system is governed by the two (or more)-dimensional mapping function, it is difficult to draw the map because the map has four dimensions, from two dimensions to two dimensions. In this study, therefore, a “two-dimensional graphical method” is proposed and the bifurcation of the two-dimensional system is visualized.