This work concerns the generalized Hopf bifurcation analysis of a piecewise-smooth wheel system with higher order discontinuities. Center manifold reduction is used to reduce the towed caster wheel system to a planar dynamical system, in which the non-smoothness factor is considered. The analysis can be divided into two cases by the coefficient of quadratic term. If the coefficient of quadratic term is equal to zero, the type of generalized Hopf bifurcation can be determined by the stability of first-order fine focus. Otherwise, we have to construct a Poincaré map for illustrating the type of generalized Hopf bifurcation, which is the heart of our discussion. Besides, we put forward another convenient way to judge the bifurcation types due to the symmetrical characteristic of this wheel system. Numerical simulations show the feasibility of theoretical analysis.

这项工作涉及具有高阶不连续性的分段光滑轮系统的广义 Hopf 分岔分析。中心歧管缩减用于将牵引脚轮系统缩减为平面动力系统，其中考虑了非光滑因素。根据二次项的系数，分析可以分为两种情况。如果二次项系数为零，则广义Hopf分岔的类型可以由一阶细焦点的稳定性决定。否则，我们必须构建一个庞加莱映射来说明广义 Hopf 分岔的类型，这是我们讨论的核心。此外，由于该轮系的对称特性，我们提出了另一种方便的判断分叉类型的方法。