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Practical Stability of Chaotic Attractors
- Chaos, Solitons & Fractals
, 1998
"... Abstract--In this paper we introduce the concept of practical stability and practical stability in finite time for chaotic attractors. The connection between practical and asymptotic stability is discussed. ..."
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Cited by 2 (0 self)
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Abstract--In this paper we introduce the concept of practical stability and practical stability in finite time for chaotic attractors. The connection between practical and asymptotic stability is discussed.
The theory of chaotic attractors
"... James Yorke won the 2003 Japan Prize for his work in the field of chaos theory. This book was compiled by four of his best-known collaborators in honor of his 60th birthday and contains papers by various authors on chaos and chaotic attractors. The papers are organized around the topics of "na ..."
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James Yorke won the 2003 Japan Prize for his work in the field of chaos theory. This book was compiled by four of his best-known collaborators in honor of his 60th birthday and contains papers by various authors on chaos and chaotic attractors. The papers are organized around the topics of "
Robust learning of chaotic attractors
"... A fundamental problem with the modeling of chaotic time series data is that minimizing short-term prediction errors does not guarantee a match between the reconstructed attractors of model and experiments. We introduce a modeling paradigm that simultaneously learns to short-tenn predict and to locat ..."
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Cited by 1 (1 self)
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A fundamental problem with the modeling of chaotic time series data is that minimizing short-term prediction errors does not guarantee a match between the reconstructed attractors of model and experiments. We introduce a modeling paradigm that simultaneously learns to short-tenn predict
Hölder regularity and chaotic attractors
, 2001
"... We demonstrate how the Hölder regularity of a given signal is a lower bound for the Grassberger-Procaccia correlation dimension of strange attractors PACS numbers: 05.45D,47.52 It is known from the celebrated work by Lorenz [1] that even low-dimensional deterministic dynamical systems may exhibit ch ..."
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chaotic behavior. In the context of turbulence in fluid dynamics, Ruelle and Takens [2] have shown that the usual attractors of the asymptotic flow in the phase-space (fixed points, periodic and quasiperiodic motion) cannot explain the sensitive dependence of the solutions on the initial conditions
Divergence Measure Between Chaotic Attractors
, 2000
"... We propose a measure of divergence of probability distributions for quantifying the dissimilarity of two chaotic attractors. This measure is defined in terms of a generalized entropy. We illustrate our procedure by considering the effect of additive noise in the well known Hénon attractor. Compariso ..."
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We propose a measure of divergence of probability distributions for quantifying the dissimilarity of two chaotic attractors. This measure is defined in terms of a generalized entropy. We illustrate our procedure by considering the effect of additive noise in the well known Hénon attractor
Chaotic attractors exhibiting quasicrystalline structure
"... An extension of canonical projection allowing the projection of objects from higher dimensional space onto quasicrystalline structures is developed. In particular, we create symmetric chaotic attractors in 5-dimensionsal space and then project them to the plane such that the resulting image exhibits ..."
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An extension of canonical projection allowing the projection of objects from higher dimensional space onto quasicrystalline structures is developed. In particular, we create symmetric chaotic attractors in 5-dimensionsal space and then project them to the plane such that the resulting image
Symmetry Breaking Bifurcations of Chaotic Attractors
- INT. J. BIF. CHAOS
, 1994
"... In an array of coupled oscillators synchronous chaos may occur in the sense that all the oscillators behave identically although the corresponding motion is chaotic. When a parameter is varied this fully symmetric dynamical state can lose its stability, and the main purpose of this paper is to inves ..."
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Cited by 7 (4 self)
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In an array of coupled oscillators synchronous chaos may occur in the sense that all the oscillators behave identically although the corresponding motion is chaotic. When a parameter is varied this fully symmetric dynamical state can lose its stability, and the main purpose of this paper
Fine structure of chaotic attractor for multiple-access communication
- Proceedings of NDES'99
, 1999
"... A method for multiple access using the structure of the unstable periodic orbits of chaotic attractor is proposed. Possible principles of the control and selection of unstable cycle-codes are presented. 1. ..."
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Cited by 2 (1 self)
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A method for multiple access using the structure of the unstable periodic orbits of chaotic attractor is proposed. Possible principles of the control and selection of unstable cycle-codes are presented. 1.
Results 1 - 10
of
1,088
