Mathematical model of a saline oscillator

We use singularity theory methods in bifurcation theory to investigate an oscillatory flow at the onset of a so-called saline oscillation. An oscillatory flow of water is generated when a cup containing saline water, with a small orifice in its base, is placed within an outer vessel containing pure water. This simple system exhibits various nonlinear characteristics, such as a limit cycle, bifurcation of the oscillatory flow and entrainment among the oscillators. We analyze the existence of a limit cycle and a bifurcation to the oscillatory flow theoretically by proposing a mathematical model of this system.