On the boundary crises of chaotic attractors in nonlinear oscillators

Computer Assisted Mechanics and Engineering Sciences

Volumn 7, Issue 4, 2000, Pages 743-755

  Tyrkiel, Elzbieta ^a   Szemplińska Stupnicka, Wanda ^a   Zubrzycki, Andrzej ^a  

^a INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY VALUE PROBLEMS; CHAOS THEORY; GEOMETRY; MATHEMATICAL MODELS; NONLINEAR SYSTEMS;

CHAOTIC ATTRACTORS; DUFFING OSCILLATOR; NONLINEAR OSCILLATORS;

OSCILLATORS (MECHANICAL);

EID: 17744413381     PISSN: 1232308X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. M.J. Feigenbaum. Quantitative universality for a class of nonlinear transformations. J. Stat. Phys., 19: 25-52, 1978.
2. C. Grebogi, E. Ott, J.A. Yorke. Crises, sudden changes in chaotic attractors and transient chaos. Physica, D7: 181-200, 1983.
3. A.L. Katz, E.H. Dowell. From single-well chaos to cross-well chaos: a detailed explanation in terms of manifold intersections. Int. J. Bifurcation and Chaos, 4(4): 933-941, 1994.
4. H.E. Nusse, J.A. Yorke. Dynamics: Numerical Explorations. Springer-Verlag, New York, 1998.
5. E. Ott. Chaos in Dynamical Systems. Cambridge University Press, Cambridge, 1993.
6. M.S. Soliman, J.M.T. Thompson. Basin organization prior to a tangled saddle-node bifurcation. Int. J. Bifurcation and Chaos, 1(1): 107-118, 1991.
7. J.C. Sommerer, C. Grebogi. Determination of crisis parameter values by direct observation of manifold tangencies. Int. J. Bifurcation and Chaos, 2(2): 383-396, 1992.
8. H.B. Stewart, Y. Ueda. Catastrophes with indeterminate outcome. Proc. Roy. Soc. Lond., A432: 113-123, 1991.
9. W. Szemplińska-Stupnicka, K.L. Janicki. Basin boundary bifurcations and boundary crisis in the twin-well Duffing oscillator: scenarios related to the saddle of the large resonant orbit. Int. J. Bifurcation and Chaos, 7(1): 129-146, 1997.
10. W. Szemplińska-Stupnicka, E. Tyrkiel. Sequences of global bifurcations and the related outcomes after crisis of the resonant attractor in a nonlinear oscillator. Int. J. Bifurcation and Chaos, 7(11): 2437-2457, 1997.
11. W. Szemplińska-Stupnicka, A. Zubrzycki, E. Tyrkiel. Properties of chaotic and regular boundary crisis in dissipative driven nonlinear oscillators. Nonlinear Dynamics, 19: 19-36, 1999.
12. W. Szemplińska-Stupnicka, E. Tyrkiel, A. Zubrzycki. Chaotic oscillations in a model of suspended elastic cable under planar excitation. Computer Assisted Mech. Engng. Sci., 6: 217-229, 1999.
13. J.M.T. Thompson, H.B. Stewart, Y. Ueda. Safe, explosive and dangerous bifurcations in dissipative dynamical systems. Phys. Rev. E 49(2): 1019-1027, 1994.
14. Y. Ueda, S. Yoshida, H.B. Stewart, J.M.T. Thompson. Basin explosions and escape phenomena in the twin-well Duffing oscillator: Compound global bifurcations organizing behavior. Phil. Trans. Roy. Soc. London A332: 169-186, 1990.