Nonstationary process: Nonstationary Bifurcation Maps, evolutionary dynamics

Nonlinear Dynamics

Volumn 21, Issue 4, 2000, Pages 337-352

  Evan Iwanowski, R M ^a   Lu, C H ^b  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

^b Dover Elevator Systems   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CONTROL SYSTEM ANALYSIS; DYNAMIC RESPONSE; INTEGRATION; PERTURBATION TECHNIQUES;

EVOLUTIONARY DYNAMICS; NONSTATIONARY BIFURCATION MAPS;

NONLINEAR CONTROL SYSTEMS;

EID: 0033884473     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008320925042     Document Type: Article

References (15)

1. Mitropolskii, Y. Y., Problems of the Asymptotic Theory of Non-Stationary Vibrations, Daniel Davey, New York, 1965.
2. Evan-Iwanowski, R. M., Resonance Oscillations in Mechanical Systems, Elsevier, Amsterdam, 1976.
3. Lu, C.-H., Evan-Iwanowski, R. M., and Jia, H. Y., 'On the stabilization of non-stationary parametric main resonance of a laminated angle-ply column', International Journal of Computers & Structures 61(4), 1996, 695-704.
4. Lu, C.-H., Mao, R., and Evan-Iwanowski, R. M., 'Non-stationary parametric responses of shear deformable orthotropic plates', Journal of Sound and Vibration 184(2), 1995, 329-342.
5. Lu, C.-H., and Evan-Iwanowski, R. M., 'The nonstationary effects on a softening Duffing oscillator', Mechanics Research Communications 21(6), 1994, 555-564.
6. Lu, C.-H., and Evan-Iwanowski, R. M., 'Period doubling bifurcation problems in the softening Duffing oscillator with nonstationary excitation', Nonlinear Dynamics 5, 1994, 401-420.
7. Evan-Iwanowski, R. M., Lu, C.-H., and Ostiguy, G. L., 'On the fundamental issues in nonstationary dynamics and chaos', in Proceedings of 14th Biennial Conference on Dynamics and Vibration of Time-Varying Systems and Structures, Albuquerque, New Mexico, September, ASME DE-Vol. 56, S. C. Sinha and R. M. Evan-Iwanowski (eds.), ASME, New York, 1993, pp. 1-12.
8. Evan-Iwanowski, R. M., Nayfeh, J. C., and Lu, C.-H., 'The nonstationary effects in asymmetric angleply laminated composite plates', in Proceedings of 14th Biennial Conference on Nonlinear Vibration, Albuquerque, New Mexico, September, ASME DE-Vol. 54, S. C. Sinha and R. M. Evan Iwanowski (eds.), ASME, New York, 1993, pp. 277-286.
9. Moslehy, F. A. and Evan-Iwanowski, R. M., 'The effects of non-stationary processes on chaotic and regular responses of the Duffing oscillator', International Journal of Non-Linear Mechanics 26, 1991, 61-71.
10. Tran, M. H. and Evan-Iwanowski, R. M., 'Non-stationary response of self-excited driven system', International Journal of Non-Linear Mechanics 25, 1990, 285-297.
11. Evan-Iwanowski, R. M. and Lu, C.-H., 'Nonstationary processes: Multiple control parameters and multiple evolution paths', in Proceedings of the Nineteenth Southeastern Conference on Theoretical and Applied Mechanics, Vol. XIX, C. T. Tsai and K. K. Stevens (eds.), Florida Atlantic University, Boca Raton, FL, 1998, pp. 553-560.
12. Ueda, Y., 'Steady motion exhibited by Duffing's equation: A picture book of regular and chaotic motions', in New Approaches to Non-Linear Problems in Dynamics, P. J. Holmes (ed.), SIAM, Philadelphia, PA, 1980, pp. 311-322.
13. Feigenbaum, M., 'Reflections of the polish masters', Los Alamos Science Fall, 1982, 55-63.
14. Kauffman, S. A., The Origins of Order, Oxford University Press, Oxford, 1993.
15. Szemplinska-Stupnicka, W., 'Bifurcations of harmonic solution leading to chaotic motion in the softening type Duffing's oscillator', International Journal of Non-Linear Mechanics 23, 1988, 257-277.