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Biomedical subjects

YC Lai

Publications and source records attributed to YC Lai.

At least 19 recordsLinked to original sources
PubMed2000

Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series

A practical and popular technique to extract the symbolic dynamics from experimentally measured chaotic time series is the threshold-crossing method, by which an arbitrary partition is utilized for determining the symbols. We address to what extent the symbolic dynamics so obtained can faithfully represent the phase-space dynamics. Our principal result is that such a practice can lead to a severe misrepresentation of the dynamical system. The measured topological entropy is a Devil's staircase-like, but surprisingly nonmonotone, function of a parameter characterizing the amount of misplacement of the partition.

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PubMed2000

Estimating generating partitions of chaotic systems by unstable periodic orbits

An outstanding problem in chaotic dynamics is to specify generating partitions for symbolic dynamics in dimensions larger than 1. It has been known that the infinite number of unstable periodic orbits embedded in the chaotic invariant set provides sufficient information for estimating the generating partition. Here we present a general, dimension-independent, and efficient approach for this task based on optimizing a set of proximity functions defined with respect to periodic orbits. Our algorithm allows us to obtain the approximate location of the generating partition for the Ikeda-Hammel-Jones-Moloney map.

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PubMed2000

Topological scaling and gap filling at crisis

Scaling laws associated with an interior crisis of chaotic dynamical systems are studied. We argue that open gaps of the chaotic set become densely filled at the crisis due to the sudden appearance of unstable periodic orbits with extremely long periods. We formulate a scaling theory for the associated growth of the topological entropy.

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PubMed2000

Detecting unstable periodic orbits from transient chaotic time series

We address the detection of unstable periodic orbits from experimentally measured transient chaotic time series. In particular, we examine recurrence times of trajectories in the vector space reconstructed from an ensemble of such time series. Numerical experiments demonstrate that this strategy can yield periodic orbits of low periods even when noise is present. We analyze the probability of finding periodic orbits from transient chaotic time series and derive a scaling law for this probability. The scaling law implies that unstable periodic orbits of high periods are practically undetectable from transient chaos.

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PubMed2000

Integrated chaotic communication scheme

We present the characteristics and an analysis of a proposed communication scheme fully based on chaos theory. The key point is that the proposed scheme introduces the dynamical system as a way to encode and decode information and as a signal wave generator. In this scheme, all the protocols used to communicate digitally are fully integrated into one single design based on a chaotic modulation process. The chaotic encoder finds a set of trajectories that codes the information into a hard to decode chaotic wave form that carries a large amount of information. We also show how our scheme can handle multiplexing, which is also used as a way to enhance security, and its ability to handle noise.

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PubMed2000

Topology of high-dimensional chaotic scattering

We investigate Hamiltonian chaotic scattering in physically realistic three-dimensional potentials. We find that the basin topology of the scattering dynamics can undergo a metamorphosis from being totally disconnected to being connected as a system parameter, such as the particle energy, is varied through a critical value. The dynamical origin of the metamorphosis is investigated, and the topological change in the scattering basin is explained in terms of the change in the structure of the invariant set of nonescaping orbits. A dynamical consequence of this metamorphosis is that the fractal dimension of the chaotic set responsible for the chaotic scattering changes its behavior characteristically at the metamorphosis. This topological metamorphosis has no correspondence in two-degree-of-freedom open Hamiltonian systems.

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PubMed2000

Intermittency in chaotic rotations

We examine the rotational dynamics associated with bounded chaotic flows, such as those on chaotic attractors, and find that the dynamics typically exhibits on-off intermittency. In particular, a properly defined chaotic rotation tends to follow, approximately, the phase-space rotation of a harmonic oscillator with occasional bursts away from this nearly uniform rotation. The intermittent behavior is identified in several well studied chaotic systems, and an argument is provided for the generality of this behavior.

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PubMed2000

Catastrophe of riddling

Most existing works on riddling assume that the underlying dynamical system possesses an invariant subspace. We find that, under arbitrarily small, deterministic perturbations, a riddled basin is typically destroyed and replaced by fractal ones, a catastrophe of riddling. We elucidate, based on analyzing unstable periodic orbits, the dynamical mechanism of the catastrophe. Analysis of the critical behaviors leads to the finding of a transient chaotic behavior that is different from those reported previously.

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