NONLINEAR OSCILLATIONS AND CHAOTIC MOTIONS IN A ROAD VEHICLE SYSTEM WITH DRIVER STEERING CONTROL

The nonlinear dynamics of a differential system describing the motion of a vehicle driven by a pilot is examined. In a first step, the stabi lity of the system near the critical speed is analyzed by the bifurcat ion method in order to characterize its behavior after a loss of stabi lity. It is shown that a Hopf bifurcation takes place, the stability o f limit cycles depending mainly on the vehicle and pilot model paramet ers. In a second step, the front wheels of the vehicle are assumed to be subjected to a periodic disturbance. Chaotic and hyperchaotic motio ns are found to occur for some range of the speed parameter. Numerical simulations, such as bifurcation diagrams, Poincare maps, Fourier spe ctrums, projection of trajectories, and Lyapunov exponents are used to establish the existence of chaotic attractors. Multiple attractors ma y coexist for some values of the speed, and basins of attraction for s uch attractors are shown to have fractal geometries.