Bifurcation dynamics of three-dimensional systems

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 10, Issue 8, 2000, Pages 1787-1804

  Phillipson, Paul E ^a,b   Schuster, Peter ^a  

^a Inst Theor Chem Molec S   (Austria)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034238507     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127400001122     Document Type: Article

References (24)

1. Arneodo, A., Coullet, P. & Tressor, C. [1980] "Occurrence of strange attractors in three-dimensional Volterra equations," Phys. Lett. A79, 259-263.
2. Arneodo, A., Coullet, P. H., Spielgel, E. A. & Tresser, C. [1985] "Asymptotic chaos," Physica D14, 327-347.
3. Chua, L. O. [1992] "The genesis of Chua's circuit," Archiv fur Electronik und Ubertragungstechnik 46, 250-257.
4. Holmes, C. & Holmes, P. [1981] "Second order averaging and bifurcations to subharmonics in Duffing's equation," J. Sound Vib. 78, 161-174.
5. Hofbauer, J. [1981] "On the occurrence of limit cycles in the Volterra-Lotka equation," Anal. Th. Methods Appl. 5, 1003-1007.
6. Hofbauer, J. & Sigmund, K. [1988] The Theory of Evolution and Dynamical Systems (Cambridge University Press, NY).
7. Iooss, G. & Joseph, D. [1990] Elementary Stability and Bifurcation Theory (Springer-Verlag, NY), Chap. XI.
8. Jackson, E. A. [1991] Perspectives in Nonlinear Dynamics (Cambridge University Press, NY).
9. Khibnik, A. I., Roose, D. & Chua, L. O. [1993] "The periodic orbits and homoclinic bifurcations in Chua's circuit with a smooth nonlinearity," in Chua's Circuit: A Paradigm for Chaos, ed. Madan, R. N. (World Scientific, Singapore), pp. 145-178.
10. Krylov, N. M. & Bogoliubov, N. N. [1947] Introduction to Nonlinear Mechanics (Princeton University Press, Princeton, NJ).
11. Kubiček, M. & Marek, M. [1983] Computational Methods in Bifurcation Theory and Dissipative Structures (Springer-Verlag, NY).
12. Lorenz, E. N. [1963] "Deterministic nonperiodic flow," J. Atmos. Sci. 20, 130-141.
13. Madan, R. N. & Wu, C. W. [1993] "Introduction to experimental chaos using Chua's circuit," in Chua's Circuit: A Paradigm for Chaos, ed. Madan, R. N. (World Scientific, Singapore), pp. 59-89.
14. Metropolis, N., Stein, M. L. & Stein, P. R. [1973] "On finite limit sets for transformations on the unit interval," J. Combinat. Th. A15, 25-44.
15. Michielin, O. & Phillipson, P. E. [1994] "Construction of Poincaré maps for multiply periodic and chaotic flows," Phys. Lett. A188, 309-316.
16. Michielin, O. & Phillipson, P. E. [1997] "Map dynamics study of the Lorenz equations," Int. J. Bifurcation and Chaos 7, 373-382.
17. Peitgen, H.-O., Jürgens, H. & Saupe, D. [1992] Chaos and Fractals, New Frontiers of Science (Springer-Verlag, NY).
18. Petrov, V., Scott, S. K. & Showalter, K. [1992] "Mixed-mode oscillations in chemical systems," J. Chem. Phys. 97, 6191-6198.
19. Phillipson, P. E. & Schuster, P. [1994] "Map dynamics of autocatalytic networks and the replicator equations," J. Math. Biol. 32, 545-562.
20. Phillipson, P. E. & Schuster, P. [1998] "Analytics of bifurcation," Int. J. Bifurcation and Chaos 8, 471-482.
21. Rössler, O. E. [1976] "An equation for continuous chaos," Phys. Lett. A57, 397-398.
22. Schnabl, W., Stadler, P. F., Forst, C. & Schuster, P. [1991] "Full characterization of a strange attractor," Physica D48, 65-90.
23. Schuster, P., Sigmund, K. & Wolff, R. [1980] "Mass action kinetics of selfreplication in flow reactors," J. Math. Anal. Appl. 78, 88-112.
24. Sparrow, C. [1982] The Lorenz Equations: Bifurcations, Chaos and Strange Attractors (Springer-Verlag, NY).