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Volumn 58, Issue 2, 1998, Pages 1724-1736

Dynamics of coding in communicating with chaos

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Indexed keywords


EID: 0001082245     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.58.1724     Document Type: Article
Times cited : (44)

References (27)
  • 5
    • 85036206425 scopus 로고    scopus 로고
    • The Mathematical Theory of Communication (The University of Illinois Press, 1964)
    • C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (The University of Illinois Press, 1964).
    • Shannon, C.E.1    Weaver, W.2
  • 8
    • 85036279775 scopus 로고    scopus 로고
    • It should be noted that [Formula Presented] is not a proof that a system is random since deterministic chaotic systems may also have a topological entropy of [Formula Presented] For instance, the topological entropy of the logistic map at [Formula Presented] is equal to [Formula Presented] but the logistic map is deterministic
    • It should be noted that hT=ln 2 is not a proof that a system is random since deterministic chaotic systems may also have a topological entropy of ln 2. For instance, the topological entropy of the logistic map at r=4 is equal to ln 2, but the logistic map is deterministic.
  • 12
    • 45949120176 scopus 로고
    • For chaotic sets arising in two-dimensional invertible maps, every point on the set has a stable and an unstable direction. Distances along the stable (the unstable) direction shrink (expands) on the average exponentially in time. A chaotic set is hyperbolic if there is a stable and an unstable direction at each point of the set, and the angle between them is bounded away from zero. Otherwise the set is nonhyperbolic. In general, nonhyperbolicity is a complicating feature because it can cause fundamental difficulties in the study of the chaotic systems, a known one being the shadowability of numerical trajectories by true trajectories [see, for example, C. Grebogi, S. M. Hammel, and J. A. Yorke, J. Complexity 3, 136 (1987)
    • (1987) J. Complexity , vol.3 , pp. 136
    • Grebogi, C.1    Hammel, S.M.2    Yorke, J.A.3
  • 21
    • 85036185638 scopus 로고    scopus 로고
    • P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Progress in Physics Vol. I (Birkhäuser, Boston, 1980)
    • P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Progress in Physics Vol. I (Birkhäuser, Boston, 1980).
  • 22
    • 85036226572 scopus 로고    scopus 로고
    • B.-L. Hao, Elementary Symbolic Dynamics and Chaos in Dissipative Systems (World Scientific, Singapore, 1989)
    • B.-L. Hao, Elementary Symbolic Dynamics and Chaos in Dissipative Systems (World Scientific, Singapore, 1989).
  • 26
    • 85036150773 scopus 로고    scopus 로고
    • See also, J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983)
    • See also, J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.