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The Study Of Bifurcations Through The Solution Of The Fokker-Planck Equation

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IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics

Part of the book series: Solid Mechanics and its Applications ((SMIA,volume 47))

Abstract

The solution of the Fokker-Planck equation of a nonlinear dynamical system is pursued by a cell-method. The purpose is to conduct a bifurcation analysis of the system. Some numerical examples are discussed.

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References

  • Baker G.L., Gollub J.P., Chaotic Dynamics. An Introduction., Cambridge University Press, 1990

    MATH  Google Scholar 

  • Birkhoff G., Rota G.C., Ordinary Differential Equations., John Wiley k Sons, 1959

    Google Scholar 

  • Bolotin V.V., Statistical Methods in Structural Mechanics., Holden-Day Inc., San Francisco, 1969

    MATH  Google Scholar 

  • Casciati F. (ed.), Dynamic Motion: Chaotic and Stochastic Behaviour., CISM Courses and Lectures No.340, Springer-Verlag, Berlin, 1993

    Google Scholar 

  • Casciati F., Faravelli L., Fragility Analysis of Complex Structural Systems., Research Studies Press, Tauton, 1990

    Google Scholar 

  • Caughey T.K., Nonlinear Theory of Random Vibrations., in Advances in Applied Mechanics Vol.11, Chia-Shu Yih (ed.), Academic Press, 1971

    Google Scholar 

  • Crandall S.H., Chandiramani K.L. and Cook R.G., Some First-Passage Problems in Random Vibration, Journal of Applied Mechanics, Transaction of ASME, 532–538, 1966

    Google Scholar 

  • Gould H., Tobochnik J., An Introduction to Computer Simulation Methods., Addison- Wesley Publishing Company, Inc., Reading Massachusetts, USA, 1987

    Google Scholar 

  • Griffiths D.V., Smith I.M., Numerical Methods for Engineers., Blackwell Scientific Publications, 1991

    Google Scholar 

  • Hsu C.S., Chiu H.M., Global Analysis of a System with multiple Responses including a strange attractor., Journal of Sound and Vibration, Vol. 114(2), 203–218, 1987

    Article  MathSciNet  Google Scholar 

  • Kreutzer E., Analysis of Chaotic Systems Using the Cell Mapping Approach., Ingenieur- Archiv, Vol. 55, 285–294, 1985

    Article  Google Scholar 

  • Kunert A., Pfeiffer F., Description of Chaotic Motion by an Invariant Distribution at the Example of the Driven Duffing Oscillator., International Series of Numerical Mathematics, Vol.97, Birkhauser Verlag Basel, 1991

    Google Scholar 

  • Langtangen H.P., A General Numerical Solution Method for Fokker-Planck Equations with Applications to Structural Reliability., Probabilistic Engineering Mechanics, Vol.6, No.l, 33–48, 1991

    Article  Google Scholar 

  • Lin K., Probabilistic Theory of Structural Dynamics., Robert E. Krieger Publishing Company, 1976

    Google Scholar 

  • Naess A., Johnsen J.N., 1991, The Path Integral Solution Technique applied to the Random Vibration of Hysteretic System., in Computational Stochastic Mechanics, P.D. Spanos and C.A. Brebbia eds., Computational Mechanics, Southampton

    Google Scholar 

  • Spencer B.F., Bergman L.A., On the Reliability of a simple Hysteretic System., Journal of Engineering Mechanics, ASCE, Vol.111, No.12, December, 1985

    Google Scholar 

  • Spencer B.F., Bergman L.A., On the Numerical Solution of the Fokker-Planck Equation for Nonlinear Stochastic Systems, Nonlinear Dynamics, Vol. 4, No. 5, 357–372, 1993

    Article  Google Scholar 

  • Tongue B.H., A Multiple-Map Strategy for Interpolated Mapping., Int. J. Non-Linear Mechanics, Vol.25, No.2/3, pp.177–186, 1990

    Article  MathSciNet  Google Scholar 

  • Wedig W., Vom Chaos zur Ordnung., GAMM - Mitteilungen, Heft 2, 3–31, 1988

    Google Scholar 

  • Wedig W., Analysis and Simulation of Nonlinear Stochastic Systems., Proceedings of the IUTAM Symposium on Nonlinear Dynamics in Engineering Systems, Springer Verlag, Berlin, 1989

    Google Scholar 

  • Wen Y.K., Stochastic Response and Damage Analysis of Inelastic Structures. Probabilistic Engineering Mechanics, Vol.1, No.l, 49–57, 1986

    Article  Google Scholar 

  • Whitney C.A., Random Processes in Physical Systems., John Wiley & Sons, 1990

    MATH  Google Scholar 

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© 1996 Kluwer Academic Publishers

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Bontempi, F., Faravelli, L. (1996). The Study Of Bifurcations Through The Solution Of The Fokker-Planck Equation. In: Naess, A., Krenk, S. (eds) IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics. Solid Mechanics and its Applications, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0321-0_7

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  • DOI: https://doi.org/10.1007/978-94-009-0321-0_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6630-3

  • Online ISBN: 978-94-009-0321-0

  • eBook Packages: Springer Book Archive

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