Discontinuous bifurcations of chaotic attractors in forced oscillators by Generalized Cell Mapping Digraph (GCMD) method

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 11, Issue 3, 2001, Pages 723-736

  Hong, Ling ^a   Xu, Jianxue ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035638070     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127401002419     Document Type: Article

References (23)

1. Abraham, R. H. [1985] "Chaostrophes, intermittency and noise," in Chaos, Fractals, and Dynamics, eds. Fischer, P. & Smith, W. R. (Dekker, NY), pp. 3-22.
2. Abraham, R. H. & Stewart, H. B. [1986] "A chaotic blue sky catastrophe in forced relaxation oscillations," Physica D19, 394-400.
3. Abraham, R. H. & Shaw, C. D. [1992] Dynamics: The Geometry of Behavior (Addison-Wesley, Redwood City, CA).
4. Grebogi, C., Ott, E. & Yorke, J. A. [1983] "Crises, sudden changes in chaotic attractors, and transient chaos," Physica D7, 181-200.
5. Grebogi, C., Ott, E. & Yorke, J. A. [1986] "Critical exponents of chaotic transients in nonlinear dynamical systems," Phys. Rev. Lett. 57, 1284-1287.
6. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, NY).
7. Hong, L. & Xu, J. [1999] "Crises and chaotic transients studied by the generalized cell mapping digraph method," Phys. Lett. A262(4&5), 361-375.
8. Hsu, C. S. [1987] Cell-to-Cell Mapping: A Method of Global Analysis for Nonlinear Systems (Springer-Verlag, NY).
9. Hsu, C. S. [1992] "Global analysis by cell mapping," Int. J. Bifurcation and Chaos 2(4), 727-771.
10. Hsu, C. S. [1995] "Global analysis of dynamical systems using posets and digraphs," Int. J. Bifurcation and Chaos 5(4), 1085-1118.
11. Jiang, J. & Xu, J. [1994] "A method of point mapping under cell reference for global analysis of nonlinear dynamical systems," Phys. Lett A188, 137-145.
12. Jiang, J. & Xu, J. [1996] "An iterative method of point mapping under cell reference for the global analysis of nonlinear dynamical systems," J. Sound Vibr. 194, 605-621.
13. Lai, Y.-C., Grebogi, C. & Yorke, J. A. [1992] "Sudden change in the size of chaotic attractors: How does it occur?" in Applied Chaos, eds. Kim, J. H. & Stringer, J. (Wiley, NY), pp. 441-455.
14. Simó, C. [1979] "On the Hénon-Pomeau attractor," J. Stat. Phys. 21, 465-494.
15. Stewart, H. B. [1988] "A chaotic saddle catastrophe in forced oscillators," in Dynamical Systems Approaches to Nonlinear Problems in Systems and Circuits, eds. Salam, F. & Levi, M. (SIAM, Philadelphia), pp. 138-149.
16. Thompson, J. M. T. & Stewart, H. B. [1986] Nonlinear Dynamics and Chaos (Wiley, Chichester).
17. Thompson, J. M. T., Stewart, H. B. & Ueda, Y. [1994] "Safe, explosive, and dangerous bifurcations in dissipative dynamical systems," Phys. Rev. E49, 1019-1027.
18. Tongue, B. H. [1987] "On obtaining global nonlinear system characteristics through interpolated cell mapping," Physica D28, 401-408.
19. Tongue, B. H. & Gu, K. Q. [1988] "A higher order method of interpolated cell mapping," J. Sound Vibr. 125, 169-179.
20. Ueda, Y. [1980a] "Steady motions exhibited by Duffing's equation: A picture book of regular and chaotic motions," in New Approaches to Nonlinear Problems in Dynamics, ed. Holmes, P. J. (SIAM, Philadelphia), pp. 311-322.
21. Ueda, Y. [1980b] "Explosion of strange attractors exhibited by Duffing's equation," in Nonlinear Dynamics, ed. Helleman, R. H. G. (New York Academy of Sciences, NY), pp. 422-434.
22. Xu, J. & Hong, L. [1999] "Generalized cell mapping digraph method for global analysis of nonlinear dynamical systems," Chinese J. Acta Mech. Sin. 31(6), 724-730.
23. Zeeman, E. C. [1982] "Bifurcation and catastrophe theory," in Papers in Algebra, Analysis and Statistics, ed. Lidl, R. (American Mathematical Society, Providence, R. I.), pp. 207-272.