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THE GENERALIZED HÉNON MAPS: EXAMPLES FOR HIGHER-DIMENSIONAL CHAOS

HENDRIK RICHTER

Fraunhofer-Institut für Produktionstechnik und Automatisierung, Nobelstrasse 12, D-70569 Stuttgart, Germany

https://doi.org/10.1142/S0218127402005121Cited by:74 (Source: Crossref)

Abstract

The generalized Hénon maps (GHM) are discrete-time systems with given finite dimension, which show chaotic and hyperchaotic behavior for certain parameter values and initial conditions. A study of these maps is given where particularly higher-dimensional cases are considered.

Keywords:

References

G. Baier and M. Klein, Phys. Lett. A 151, 281 (1990). Crossref, Web of Science, Google Scholar
M. Benedicks and L. Carleson, Ann. Math. 133, 73 (1991). Crossref, Web of Science, Google Scholar
J. P. Crutchfield and K. Kaneko, Directions in Chaos 1, ed. B. L. Hao (World Scientific, Singapore, 1987) pp. 272–353. Link, Google Scholar
H. R. Dullin and J. D. Meiss, Physica D 143, 262 (2000). Crossref, Web of Science, Google Scholar
E. Fick, M. Fick and G. Hausmann, Phys. Rev. A 44, 2469 (1991). Crossref, Web of Science, Google Scholar
P. Fredericksonet al., J. Diff. Eqs. 49, 185 (1983). Crossref, Web of Science, Google Scholar
A. Fulinkski and A. S. Kleczkowski, Phys. Scr. 35, 119 (1987). Crossref, Web of Science, Google Scholar
K. T. Hansen and P. Cvitanovic, Nonlinearity 11, 1233 (1998). Crossref, Web of Science, Google Scholar
M. Hénon, Commun. Math. Phys. 50, 69 (1976). Crossref, Web of Science, Google Scholar
H. Kaplan, Phys. Rev. E 48, 1655 (1993). Crossref, Web of Science, Google Scholar
M. Klein, G. Baier and O. E. Rössler, Chaos Solit. Fract. 1, 105 (1991). Crossref, Google Scholar
T. Meyeret al., Phys. Rev. E 56, 5069 (1997). Crossref, Web of Science, Google Scholar
K. Ogata , Discrete–Time Control Systems , 2nd edn. ( Prentice Hall , Englewood Cliffs, NJ , 1995 ) . Google Scholar
H. Richter and K. J. Reinschke, Physica D 144, 309 (2000). Crossref, Web of Science, Google Scholar
R. Shaw, Z. Naturforsch. 36a, 80 (1981). Google Scholar
D. Sterling, H. R. Dullin and J. D. Meiss, Physica D 134, 153 (1999). Crossref, Web of Science, Google Scholar
A. Torciniet al., Physica D 53, 85 (1991). Crossref, Web of Science, Google Scholar