The most probable response, which acts as a deterministic geometric tool for the response analysis of stochastic systems, offers an attractive alternative to traditional methods for analyzing the P-bifurcation of the stochastic impact system. Specifically, the stochastic impact system perturbed by multiplicative Gaussian white noises is considered to research the P-bifurcations under the most probable response angle. Firstly, the non-smooth coordinate transformation of state variables is applied to convert the impact system into an equivalent system without the velocity jump. Then, the stochastic averaging method of energy envelope is exploited to the transformed system and the most probable response is obtained by the combination of the Fokker-Planck equation and the extreme value theory. Finally, based on the most probable response, the bifurcation behavior of the stochastic impact system is investigated qualitatively from a new perspective. It is found that the stochastic P-bifurcation can be induced or suppressed by modulating the noise intensity $D_2$ or the restitution coefficient $r$ in the stochastic impact system. However, there is no influence of the noise intensity $D_1$ on the most probable response of the stochastic impact system. Therefore, the noise intensity $D_1$ will not trigger the P-bifurcation of the stochastic impact system. Meanwhile, the validity of the proposed procedure is verified by numerical simulation.

最可能的响应充当随机系统响应分析的确定性几何工具，它为分析随机冲击系统的P分叉的传统方法提供了一种有吸引力的替代方法。具体而言，考虑了乘性高斯白噪声干扰的随机冲击系统，以研究在最可能的响应角下的P分叉。首先，应用状态变量的非平滑坐标变换将冲击系统转换为等效系统而没有速度跳跃。然后，将能量包络线的随机平均方法应用于转换后的系统，并通过Fokker-Planck方程和极值理论的组合获得最可能的响应。最后，根据最可能的响应，从一个新的角度定性地研究了随机冲击系统的分叉行为。可以发现，通过调节噪声强度可以诱发或抑制随机的P分叉。$d_2$ 或恢复系数 $\mathrm{[R}$在随机冲击系统中。但是，不受噪声强度的影响$d_{\mathrm{1个}}$对随机冲击系统最可能的反应。因此，噪声强度$d_{\mathrm{1个}}$不会触发随机冲击系统的P分叉。同时，通过数值模拟验证了所提方法的有效性。