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Huang, Dongwei; Wang, Hongli; Zhu, Zhiwen; Zhang, Feng

Stochastic stability of four-wheel-steering system. (English) Zbl 1131.70010

Chaos Solitons Fractals 33, No. 3, 823-828 (2007).
Summary: A four-wheel-steering system subjected to white noise excitations was reduced to a two-degree-of-freedom quasi-non-integrable-Hamiltonian system. Subsequently, we obtained a one-dimensional Itô stochastic differential equation for the averaged Hamiltonian of the system by using the stochastic averaging method for quasi-non-integrable-Hamiltonian systems. Thus, the stochastic stability of four-wheel-steering system was analyzed by analyzing the sample behaviors of the averaged Hamiltonian at the boundary \(H = 0\) and by calculating its Lyapunov exponent. An example given at the end demonstrates our conclusions.

MSC:

70L05 Random vibrations in mechanics of particles and systems
70H14 Stability problems for problems in Hamiltonian and Lagrangian mechanics

Keywords:

quasi-non-integrable-Hamiltonian system; Itô stochastic differential equation; Lyapunov exponent
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Full Text: DOI

References:

[1] Zhu, W. Q.; Huang, Z. L., Stochastic stability of quasi-nonintegrable-Hamiltonian systems, J Sound Vib, 218, 5, 769-789 (1998) · Zbl 1235.70212
[2] Zhu, W. Q.; Yang, Y. Q., Stochastic averaging of quasi-nonintegrable-Hamiltonian systems, J Appl Mech, 64, 2, 157-164 (1997) · Zbl 0902.70013
[3] Huber, M. T.; Krieg, J. C.; Braun, H. A., Noise, nonlinear dynamics and the time course of affective disorders, Chaos, Solitons & Fractals, 11, 12, 923-1928 (1999)
[4] Porsezian, K., Nonlinear Schrödinger family on moving space curves: Lax pairs, soliton solution and equivalent spin chain, Chaos, Solitons & Fractals, 9, 10, 1709-1722 (1998) · Zbl 0934.35177
[5] Rameshi, M.; Narayanan, S., Chaos control by nonfeedback methods in the presence of noise, Chaos, Solitons & Fractals, 10, 9, 1473-1489 (1999) · Zbl 0983.37040
[6] Daya Sagar, B. S., Morphological evolution of a pyramidal sandpile through bifurcation theory: A qualitative model, Chaos, Solitons & Fractals, 10, 9, 1559-1566 (1999) · Zbl 0961.92040
[7] Ahmed, E.; El-Misiery, A.; Agiza, H. N., On controlling chaos in an inflation-unemployment dynamical system, Chaos, Solitons & Fractals, 10, 9, 1567-1570 (1999) · Zbl 0958.91042
[8] Richter, Hendrik; Stein, Günter, On Taylor series expansion for chaotic nonlinear systems, Chaos, Solitons & Fractals, 13, 9, 1783-1789 (2002) · Zbl 0999.65145
[9] Helal, M. A., Soliton solution of some nonlinear partial differential equations and its applications in fluid mechanics, Chaos, Solitons & Fractals, 13, 9, 1917-1929 (2002) · Zbl 0997.35063
[10] Wagg, D. J., Periodic and chaotic dynamics in an asymmetric elastoplastic oscillator, Chaos, Solitons & Fractals, 16, 5, 779-786 (2003) · Zbl 1104.74312
[11] Ke-Fei, Cao; Xu-Sheng, Zhang; Zhong, Zhou; Shou-Li, Peng, Devil’s carpet of topological entropy and complexity of global dynamical behavior, Chaos, Solitons & Fractals, 16, 5, 709-726 (2003) · Zbl 1030.37023
[12] Zhu, W. Q.; Huang, Z. L., Stochastic Hopf bifurcation of quasi-nonintegrable-Hamiltonian systems, Int J Non-Linear Mech, 34, 437-447 (1999) · Zbl 1342.70072
[13] Cai, G. Q.; Lin, Y. K., Random vibration of strongly nonlinear systems, Nonlinear Dynam, 24, 3, 3-15 (2001) · Zbl 0982.70017
[14] Yu, Zh. Sh., Vehicle Theory (1994), Mechanism Industrial Publishing House: Mechanism Industrial Publishing House Beijing, China, [in Chinese]
[15] Zhu, W. Q., Random Vibration (1992), Science Press: Science Press Beijing, China, [in Chinese]
[16] Zhu, W. Q., Nonlinear stochastic dynamics and control - Framework of Hamiltonian Theory (2003), Science Press: Science Press Beijing, China, [in Chinese]
[17] Zhu, W. Q., Feedback stabilization of quasi nonintegrable Hamiltonian systems by using Lyapunov exponent, Nonlinear Dynam, 36, 455-470 (2004) · Zbl 1092.70021
[18] Dong-Wei Huang, Hong-Li Wang, Yu Qiao, Zhi-Wen Zhu, Stochastic Hopf bifurcation of four-wheel-steering system, advances in stochastic structural dynamics. In: Proc of the Fifth Int Conf on Stochastic Structural Dynamics SSD03 (2003) 206-14.; Dong-Wei Huang, Hong-Li Wang, Yu Qiao, Zhi-Wen Zhu, Stochastic Hopf bifurcation of four-wheel-steering system, advances in stochastic structural dynamics. In: Proc of the Fifth Int Conf on Stochastic Structural Dynamics SSD03 (2003) 206-14.
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