Low-dimensional chaos in high-dimensional phase space: How does it occur?

Chaos, Solitons and Fractals

Volumn 15, Issue 2, 2003, Pages 219-232

  Lai, Ying Cheng ^a,b   Bollt, Erik M ^c   Liu, Zonghua ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

^b Arizona State University   (United States)

^c UNITED STATES NAVAL ACADEMY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; LYAPUNOV METHODS; PARTIAL DIFFERENTIAL EQUATIONS; SYNCHRONIZATION;

CHAOTIC SYSTEMS;

CHAOS THEORY;

EID: 0242367511     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(02)00094-2     Document Type: Article

References (52)

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3. There are so many examples of low-dimensionally chaotic dynamics occurring in high-dimensional phase space that we do not attempt to give even a partial list of the literature. An example is the magnetic ribbon system that has been used to verify a variety of low-dimensionally chaotic phenomena. See, for instance Ditto W.L.et al. Phys. Rev. Lett. 63:1989;923. and Ditto W.L., Rauseo S.N., Spano M.L. Phys. Rev. Lett. 65:1990;3211.
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9. While the phenomenon of synchronous chaos was first reported in Ref. [5], it was independently discovered and it was pointed out for the first time in the following paper that the phenomenon can have potential application in nonlinear digital communication Pecora L.M., Carroll T.L. Phys. Rev. Lett. 64:1990;821. Since then, synchronization in chaotic systems has become one of the most active research areas in nonlinear dynamics. See, for example Ditto W.L., Showalter K. Chaos (Focus Issue on Control and Synchronization of Chaos). 7:1997;509.
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