Nonlinear Dynamics

, Volume 9, Issue 3, pp 281–304 | Cite as

Nonlinear oscillations and chaotic motions in a road vehicle system with driver steering control

  • Z. Liu
  • G. Payre
  • P. Bourassa


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

Key words

Vehicle dynamics Hopf bifurcation chaotic motion fractal basin boundaries 


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Z. Liu
    • 1
  • G. Payre
    • 1
  • P. Bourassa
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of SherbrookeSherbrookeCanada

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