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采用平流层准地转－β通道近似下的波流相互作用模型，考虑大气行星波１和波２与流的相互作用，以平流层底部边界强迫波波１和波２的振幅作为参数，对该模型的分岔特性进行了研究．结果表明，系统具有稳态解支Ａ，Ｂ，Ｃ，在某些参数范围内，多种稳态解同时存在．解支Ａ对应于平流层冷冬状态，解支Ｃ对应于平流层增温状态．由于参数变化系统在稳态解Ａ和Ｃ之间发生灾变是冬季平流层暴发性增温的原因．文中给出了二维参数空间中的分岔集，它表明了对流层顶的波动对平流层暴发性增温的控制作用，能很好地解释观测事实．
Using the interaction of wave-flow interaction in stratospheric-geostrophic-β channel approximation, we consider the interaction of atmospheric planetary wave 1 and wave 2 with the flow, and the amplitudes of forced wave 1 and wave 2 are forced by the bottom of the stratosphere as parameters. The bifurcation characteristics of this model are studied. The results show that the system has steady solutions A, B, C, and in some parameters, many kinds of steady solutions exist simultaneously. Solution branch A corresponds to the stratosphere cold winter state, branch C corresponds to the stratospheric warming state. The catastrophic change between the steady-state solutions A and C due to the change of parameters is the reason for the sudden warming of the stratosphere in winter. The bifurcation set in the two-dimensional parameter space is given in this paper, which shows that the control of the stratospheric turbulence over the upper troposphere can explain the observed fact well.