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
Birkhoff G., Rota G.C., Ordinary Differential Equations., John Wiley k Sons, 1959
Bolotin V.V., Statistical Methods in Structural Mechanics., Holden-Day Inc., San Francisco, 1969
Casciati F. (ed.), Dynamic Motion: Chaotic and Stochastic Behaviour., CISM Courses and Lectures No.340, Springer-Verlag, Berlin, 1993
Casciati F., Faravelli L., Fragility Analysis of Complex Structural Systems., Research Studies Press, Tauton, 1990
Caughey T.K., Nonlinear Theory of Random Vibrations., in Advances in Applied Mechanics Vol.11, Chia-Shu Yih (ed.), Academic Press, 1971
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
Gould H., Tobochnik J., An Introduction to Computer Simulation Methods., Addison- Wesley Publishing Company, Inc., Reading Massachusetts, USA, 1987
Griffiths D.V., Smith I.M., Numerical Methods for Engineers., Blackwell Scientific Publications, 1991
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
Kreutzer E., Analysis of Chaotic Systems Using the Cell Mapping Approach., Ingenieur- Archiv, Vol. 55, 285–294, 1985
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
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
Lin K., Probabilistic Theory of Structural Dynamics., Robert E. Krieger Publishing Company, 1976
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
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
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
Tongue B.H., A Multiple-Map Strategy for Interpolated Mapping., Int. J. Non-Linear Mechanics, Vol.25, No.2/3, pp.177–186, 1990
Wedig W., Vom Chaos zur Ordnung., GAMM - Mitteilungen, Heft 2, 3–31, 1988
Wedig W., Analysis and Simulation of Nonlinear Stochastic Systems., Proceedings of the IUTAM Symposium on Nonlinear Dynamics in Engineering Systems, Springer Verlag, Berlin, 1989
Wen Y.K., Stochastic Response and Damage Analysis of Inelastic Structures. Probabilistic Engineering Mechanics, Vol.1, No.l, 49–57, 1986
Whitney C.A., Random Processes in Physical Systems., John Wiley & Sons, 1990
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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
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