Stability and Bautin bifurcation of four-wheel-steering vehicle system with driver steering control

In this paper, the lateral stability and Bautin bifurcation of a four-wheel-steering(4WS) vehicle system, by considering driver steering control, are investigated. By using the central manifold theory and projection method, the first and second Lyapunov coefficients are calculated to predict the type of Hopf bifurcation of the vehicle system. The topological structure of the Bautin bifurcation, a degenerate Hopf bifurcations of the 4WS vehicle system is presented in the parameter space and it reveals the dynamics of the vehicle system of different choices of the control parameters. The influences of system parameters on critical values of the bifurcation parameter are also analyzed. It is shown that with the increase of the frontal visibility distance of the driver control strategy coefficient and the cornering stiffness coefficients of the rear wheels, the critical speed increases. Nevertheless, the critical speed decreases with the increase of the distance from the center of gravity of the vehicle to the front axles, Driver’s perceptual time delay, and cornering stiffness coefficients of the front wheels.