Chaos and nonlinear stochastic dynamics

Probabilistic Engineering Mechanics

Volumn 15, Issue 1, 2000, Pages 37-47

  Naess, A ^a  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; MARKOV PROCESSES; PERTURBATION TECHNIQUES; PROBABILITY DENSITY FUNCTION; STATE SPACE METHODS; STATISTICAL MECHANICS; VECTORS; WHITE NOISE;

MARKOV DIFFUSION PROCESS; STOCHASTIC DYNAMICS;

DYNAMICS;

EID: 0033888656     PISSN: 02668920     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0266-8920(99)00007-7     Document Type: Article

References (21)

1. Guckenheimer J., Holmes P. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. 1983;Springer, Berlin.
2. Wiggins S. Introduction to applied nonlinear dynamical systems and chaos. 1990;Springer, Berlin.
3. Moon F.C. Chaotic and fractal dynamics. 1992;Wiley, New York.
4. Thomson J.M.T., Stewart H.B. Nonlinear dynamics and chaos. 1986;Wiley, New York.
5. Lasota A., Mackey M.C. Chaos, fractals and noise. 2 :1994;Springer, New York.
6. Sekar P., Narayanan S. Chaos in mechanical systems: a review, sādhanā, academy proceedings in engineering sciences. Indian Academy of Sciences. 20:1995;529-582.
7. Rudin W. Real and complex analysis. 3 :1987;McGraw-Hill, New York.
8. Ulam S.M., von Neuman J. On combination of stochastic and deterministic processes. Bull Am Math Soc. 53:1947;723-738.
9. Wong E., Hajek B. Stochastic processes in engineering systems. 1985;Springer, Berlin.
10. Kloeden P.E., Platen E. Numerical solution of stochastic differential equations. 1992;Springer, Berlin.
11. Naess A, Moe V. New techniques for path integral solution of the random vibration of nonlinear oscillators. Proceedings of the Seventh International Conference Structural Safety and Reliability. Japan: Kyoto, 1997.
12. Wehner M.F., Wolfer W.G. Numerical evaluation of path-integral solutions to Fokker-Planck equations. Phys Rev A. 27:(5):1983;2663-2670.
13. Sun J.Q., Hsu C.S. The generalized cell mapping method in nonlinear random vibration based upon short-time Gaussian approximation. J Appl Mechanics. 57:1990;1018-1025.
14. Naess A., Johnsen J.M. Response statistics of nonlinear dynamic systems by path integration. Bellomo N., Casciati F. Proceedings of the IUTAM Symposium on Nonlinear Stochastic Mechanics. 1992;401 Springer, Berlin.
15. Naess A., Johnsen J.M. Response statistics of nonlinear, compliant offshore structures by the path integral solution method. Probabilistic Engng Mech. 8:1993;91-106.
16. Köylüoglu H.U., Nielsen S.R.K., Iwankiewicz R. Response and reliability of poisson driven systems by path integration. J Engng Mech ASCE. 121:1995;117-130.
17. Yim S.C.S., Lin H. Unified analysis of complex nonlinear motions via densities. Naess A., Krenk S. Proceedings of the IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics. 1996;489 Kluwer Academic Publishers, Dordrecht.
18. Kunert A., Pfeiffer F. Description of chaotic motion by an invariant distribution as the example of the driven duffing oscillator. Int Ser Numer Math. 97:1991;225-230.
19. Lin H., Yim S.C.S. Analysis of a nonlinear system exhibiting chaotic, noisy chaotic and random behaviors. J Appl Mech. 63:1996;509-516.
20. Naess A., Hegstad B.K. Response statistics of van der Pol oscillators excited by white noise. Nonlinear Dynamics. 5:1994;287-297.
21. Holmes P.J. A nonlinear oscillator with a strange attractor. Philos Trans Roy Soc London A. 292:1979;419-448.