Spiral-plus-saddle attractors and elementary mechanisms for chaos generation

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 6, Issue 3, 1996, Pages 513-527

  Deng, Bo ^a  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030093599     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127496000229     Document Type: Article

References (18)

1. Arneodo, A., Coullet, P. & Tresser, C. [1982] "Oscillators with chaotic behavior: An illustration of a theorem by Shil'nikov," J. Stat. Phys. 27, 171-182.
2. Brunovský, P., Chow, S.-N. & Mallet-Paret, J. [1994] "Normal forms for singularly perturbed vector fields," preprint.
3. Chaika, Y. D. [1994], personal communication.
4. Deng, B. [1990] "Homoclinic bifurcations with nonhyperbolic equilibria," SIAM J. Math. Anal. 21, 693-719.
5. Deng, B. [1992] "Folding at the genesis of chaos," to appear in Proceedings of the First World Congress of Nonlinear Analysts.
6. Deng, B. [1993] "A mathematical model that mimics the bursting oscillations in pancreatic β-cells," Math. Biosciences 119(2), 241-250.
7. Deng, B. [1994] "Constructing homoclinic orbits and chaotic attractors," Int. J. Bifurcation & Chaos 4(4), 823-841.
8. Deng, B. [1995] "Constructing Lorenz type attractors through singular perturbations," Int. J. Bifurcation & Chaos 5(6), 1633-1642.
9. Ermentrout, B. [1988] PhasePlane, 3.0 (Brooks/Cole Publishing Company).
10. Fenichel, N. [1979] "Geometric singular perturbation theory for ordinary differential equations," J.D.E. 73, 309-353.
11. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York).
12. Poliashenko, M. & McKay, S. R. [1992] "Chaos due to the Shil'nikov mechanism in two coupled oscillators with nonisochronism," preprint, Dept. of Physics and Astronomy, Univ. of Maine.
13. Madan, R. [1993] Chua's Circuit: A Paradigm for Chaos (World Scientific, Singapore).
14. Rinzel, J. [1985] "Bursting oscillations in an excitable membrane model," in Ordinary and Partial Differential Equations, eds. Sleeman, B. D. & Jarvis, R. J. (Springer, New York), pp. 304-316.
15. Rössler, O. E. [1976] "Chaotic behavior in simple reaction systems," Z. Naturforsch A31, 259-264.
16. Rössler, O. E. [1979] "Continuous chaos - four prototype equations," in Bifurcation Theory and Applications in Scientific Disciplines, eds. Gurel, O. & Rössler, O. E. Annals of the New York Academy of Science 316, 376-392.
17. Sidorets, V. N. & Pentegov, I. V. [1992] "Appearance and structure of strange attractors in RLC-circuits with electric arc," (in Russian) Technical Electrodynamics 2, 28-32.
18. Terman, D. [1992] "The transition from bursting to continuous spiking in excitable membrane models," J. Nonlinear Science 2, 135-182.