A magnetic filter (MF) reflecting electrons from both sides can separatea low-temperature and low-density subplasma from a high-temperature andhigh-density main plasma. The one-dimensional numerical simulation bythe particle-in-cell code revealed that, depending on the asymmetry, theplasma divided by the MF exhibits a static state or a dynamic state (Ohi K et al 2001 Phys. Plasmas8 23). The transitionbetween the two bifurcated states is discontinuous. In the dynamic state,the autonomous potential oscillation in the subplasma is synchronizedwith the passage of the shock wave structure generated by the modulatedion beam from the main plasma. The stationary phase of the dynamic stateappears after the amplitude of the potential oscillation in thesubplasma grows exponentially from the thermal noise. In the staticstate, the system is stable to the growth of the potential oscillationin the subplasma.