Abstract
In this paper, linear stability and chaotic motion of a time-delayednonlinear vehicle system are studied. The stability is determined bycomputing the spectrum associated with a system of linear retardedfunctional differential equations, which reveals that a loss ofstability occurs following a Hopf bifurcation. Beyond the critical valuefor linear stability, the system exhibits limit cycle motions.Subharmonic, quasi-periodic and chaotic motions are observed for asystem excited by a periodic disturbance.
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References
Legouis, T., Laneville, A., Bourassa, P., and Payre, G., ‘Characterization of dynamic vehicle stability using two models of the human pilot behavior’, Vehicle System Dynamics 15, 1986, 1–18.
Guo, K. and Guan, X., ‘Modelling of driver/vehicle directional control system’, Vehicle System Dynamics 22, 1993, 141–184.
Liu, Z., Payre, G., and Bourassa, P., ‘Nonlinear oscillations and chaotic motion in a road vehicle system with driver steering control’, Nonlinear Dynamics, 9, 1996, 281–304.
McRuer, D. T. and Krendel, E., ‘Mathematical models of human pilot behavior’, NATO AGARDograph, No. 188, 1974.
Segel, L., ‘Theoretical prediction and experimental substantiation of the response of the automobile to steering control’, Proceedings of the Automation Division of the Institute of Mechanical Engineers 7, 1956–1957.
Manitius, A., Tran, H., Payre, G., and Roy, R., ‘Computation of eigenvalues associated with functional differential equations’, SIAM Journal on Scientific and Statistical Computing 8(3), 1987, 222–246.
Pacejka, H. B. and Bakker, E., ‘The magic formula tyre model’, in Proceedings of the 1st International Colloquium on Tyre Models for Vehicle Dynamics Analysis, Delft, The Netherlands, October, Swets Publishing Services, Lisse, The Netherlands, 1991, pp. 1–18, 21–22.
Oosten, J. van and Bakker, E., ‘Determination of magic formula tyre model parameters’, in Proceedings of the 1st International Colloquium on Tyre Models for Vehicle Dynamics Analysis, Delft, The Netherlands, October, Swets Publishing Services, Lisse, The Netherlands, 1991, pp. 21–22.
Bellman, R. and Cooke, K., Differential-Difference Equations, Academic Press, New York, 1963.
Malek-Zavarei, M. and Jamshidi, M., Time-Delayed Systems, Analysis, Optimization and Applications, North-Holland, Amsterdam, 1987.
Moon, F. C., Chaotic and Fractal Dynamics, Wiley, New York, 1992.
Thompson, J. T. and Stewart, H. B., Nonlinear Dynamics and Chaos, Wiley, Chichester, UK, 1986.
Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, Applied Mathematical Sciences, Vol. 42, Springer, Berlin, 1983.
Char, B.W., Geddes, K. O., Gonnet, G. H., Leong, B. L., Monagan, M. B., and Watt, S. M., Maple V Library Reference Manual, Waterloo Maple Publishing, Springer, Berlin, 1991.
Kuhn, H., A New Proof of the Fundamental Theorem of Algebra, Mathematical Programming Studies, Vol. 1, North-Holland Publ. Co., Amsterdam, 1974, pp. 148–158.
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Liu, Z., Payre, G. & Bourassa, P. Stability and Oscillations in a Time-Delayed Vehicle System with Driver Control. Nonlinear Dynamics 35, 159–173 (2004). https://doi.org/10.1023/B:NODY.0000021080.06727.f8
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DOI: https://doi.org/10.1023/B:NODY.0000021080.06727.f8