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Results 1 - 10
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17,291
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
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
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
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 6 (3 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
Research on Multi-scroll chaotic attractors synchronization technique
"... Abstract. Multi-scroll chaotic attractors synchronization technique is a research focuses in recent years. This paper focuses on multi-scroll chaotic attractors in the four-dimensional system. It uses variable feedback synchronous method to achieve the two 4-scroll chaotic attractors’ synchronizatio ..."
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Abstract. Multi-scroll chaotic attractors synchronization technique is a research focuses in recent years. This paper focuses on multi-scroll chaotic attractors in the four-dimensional system. It uses variable feedback synchronous method to achieve the two 4-scroll chaotic attractors
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.
Domain of attraction of hysteresis-series based chaotic attractors
"... This paper discusses the domain of attraction and its sensitivity for a class of chaotic attractors generated by using second-order linear systems with hysteresis-series. It is found that the domain of attraction of the chaotic attractors is determined by an unstable limit cycle. The chaotic dynamic ..."
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This paper discusses the domain of attraction and its sensitivity for a class of chaotic attractors generated by using second-order linear systems with hysteresis-series. It is found that the domain of attraction of the chaotic attractors is determined by an unstable limit cycle. The chaotic
Destruction of Chaotic Attractors in Coupled Chaotic Systems
, 2001
"... with respect to the strength of a coupling parameter. By varying the coupling parameter, we investigate the sudden break-up of HCAs in symmetrically coupled one- dimensional (1D) maps. It is found that, when the cou- pling parameter passes through a threshold value, a HCA breaks up suddenly when a ..."
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basin boundary. Hence the old basin becomes occupied by the new periodic attractor. This is in con- trast to the case of the boundary crisis [4], where the sudden destruction of both a chaotic attractor and its basin occurs when the chaotic attractor collides with its basin boundary. In order to examine
Results 1 - 10
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17,291
