Existence conditions for bifurcations of homoclinic orbits in a railway wheelset model.

This paper investigates the bifurcations of homoclinic orbits to hyperbolic saddle points in a simplified railway wheelset model with cubic and quintuple nonlinear terms. Using Melnikov's method, the sufficient conditions for the existence of the supercritical and the subcritical pitchfork bifurcations of homoclinic orbits are proven. To determine the integrability of the variational equations around homoclinic orbits in the meaning of differential Galois theory, the corresponding Fuchsian second-order differential equation for the normal variational equation and the Riemann P function are obtained. It is shown that the coefficients of the linear terms and the cubic coupling terms play a very significant role on influencing the existence of homoclinic orbits. While, the cubic coupling terms have little effect on the size of the left-hand and right-hand potential wells of homoclinic orbits. These results are beneficial to explore the key mechanism of hunting stability of a simplified railway wheelset model. • The sufficient conditions for pitchfork bifurcations of homoclinic orbits are proven. • The integrability of variational equations around homoclinic orbits is determined. • Linear and cubic coupling term coefficients affect the existence of homoclinic orbits. [ABSTRACT FROM AUTHOR]