A model of the dynamics of the Newton-Leipnik attractor

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 7, Issue 12, 1997, Pages 2723-2733

  Lofaro, Thomas ^a  

^a WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031498484     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127497001837     Document Type: Article

References (21)

1. Chavoya-Aceves, O., Angulo-Brown, F. & Pina, E. [1985] "Symbolic dynamics of the cubic maps," Physica D14, 374-386.
2. Collet, P. & Eckmann, J. P. [1980] Iterated Maps of the Interval as Dynamical Systems (Birkhauser, Boston).
3. Devaney, R. [1989] An Introduction to Chaotic Dynamical Systems, 2nd edition (Addison-Wesley, Redwood City, CA).
4. Ermentrout, G. B. [1996] XPPAUT2.5 - The Differential Equations Tool.
5. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York).
6. Lorenz, E. N. [1963] "Deterministic non-periodic flow," J. Atmos. Sci. 20, 130-141.
7. Leipnik, R. B. & Newton, T. A. [1981] "Double strange attractors in rigid body motion with linear feedback control," Phys. Lett. A86, 63-67.
8. LoFaro, T. [1997] "The dynamics of symmetric bimodal maps," Int. J. Bifurcation and Chaos 7(12), 2735-2744.
9. Mackay, R. S. & Tresser, C. [1987] "Some flesh on the skeleton: The bifurcation structure of bimodal maps," Physica D27, 412-422.
10. Milnor, J. & Thurston, R. [1988] "On iterated maps of the interval," in Lecture Notes in Mathematics, 1342, Dynamical Systems, ed. Alexander, J. C. (Springer- Verlag, New York), pp. 465-563.
11. Milnor, J. [1992] "Remarks on iterated cubic maps," Experimental Math. 1, 5-24.
12. Newton, T. A., Martin, D. & Leipnik, R. B. [1988] "A double strange attractor," in Dynamical Systems Approaches to Nonlinear Problems in Systems and Circuits, eds. Salam, F. A. & Levi, M. L. (SIAM, Philadelphia), pp. 117-127.
13. Packard, N. H., Crutchfield, J. P., Farmer, J. D. & Shaw,R. S. [1980] "Geometry from a time series," Phys. Rev. Lett. 45, 712-716.
14. Pesin, Ja. B. [1976] "Families of invariant manifolds corresponding to nonzero characteristic exponents," Math. USSR-Izv. 10, 1261-1305.
15. Pesin, Ja. B. [1977] "Characteristic Lyapunov exponents and smooth ergodic theory," Russ. Math. Surv. 32, 55-114.
16. Ringland, J. & Schell, M. [1991] "Genealogy and bifurcation skeleton for cycles of the iterated two-extremum map of the interval," SIAM J. Math. Anal. 22, 1354-1371.
17. Ringland, J. & Tresser, C. [1995] "A genealogy for finite kneading sequences of bimodal maps of the interval," Trans. AMS 347, 4599-4624.
18. Swinney, H. L. [1983] "Observations of order and chaos in nonlinear systems," Physica D7, 3-15.
19. Takens, F. [1980] "Detecting strange attractors in turbulence," in Dynamical Systems and Turbulence, Springer Lecture Notes in Mathematics, Vol. 898, ed. Rand, D. A. & Young, L. S. (Springer-Verlag, New York), pp. 366-381.
20. Wiggins, S. [1990] Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer-Verlag, New York).
21. Wolfram, S. [1991] Mathematica: A System for Doing Mathematics by Computer (Addison-Wesley, Reading, MA).