Generalized Hopf bifurcation analysis of a towed caster wheel system

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 Poincare 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.

Automated summary

This work discusses the generalized Hopf bifurcation analysis of a piecewise-smooth wheel system with higher order discontinuities, using center manifold reduction to simplify the system and considering non-smooth factors. The analysis can be divided into two cases based on the coefficient of the quadratic term, with the bifurcation type determined by the stability of the first-order fine focus or by constructing a Poincare map. Additionally, a convenient method to judge bifurcation types is proposed due to the symmetrical characteristic of the wheel system, with numerical simulations demonstrating the feasibility of theoretical analysis.