Biomedical subjects

Shawn D Pethel

Publications and source records attributed to Shawn D Pethel.

6 recordsLinked to original sources

PubMed2006

Chaos without nonlinear dynamics.

A linear, second-order filter driven by randomly polarized pulses is shown to generate a waveform that is chaotic under time reversal. That is, the filter output exhibits determinism and a positive Lyapunov exponent when viewed backward in time. The filter is demonstrated experimentally using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. This phenomenon suggests that chaos may be connected to physical theories whose underlying framework is not that of a traditional deterministic nonlinear dynamical system.

Journal Article↗

PubMed2006

Symbolic dynamics of coupled map lattices.

We present a method to reduce the [FORMULA: SEE TEXT] dynamics of coupled map lattices (CMLs) of N invertibly coupled unimodal maps to a sequence of N-bit symbols. We claim that the symbolic description is complete and provides for the identification of all fixed points, periodic orbits, and dense orbits as well as an efficient representation for studying pattern formation in CMLs. We give our results for CMLs in terms of symbolic dynamical concepts well known for one-dimensional chaotic maps, including generating partitions, Gray orderings, and kneading sequences. An example utilizing coupled quadratic maps is given.

Journal Article↗

PubMed2005

Complete and flexible replacement of chaotic uncertainty with transmitted information.

Natural chaos can be described as an information source emitting symbolic sequences with positive entropy. We use two algorithmic techniques from data compression in a nonstandard way along with a control scheme to replace the natural uncertainty in chaotic systems with an arbitrary digital message. Unlike previous targeting-based control, the controlled, deterministic, transmission appears statistically identical to natural chaos, with a message modulated on it at the intrinsic Kolmogorov-Sinai information generation rate of the chaotic oscillator. Thus, chaotic communication by targeting need not consume any additional channel capacity beyond that required by the message itself and the message-bearing signal may appear identical to the uncontrolled oscillator. We also demonstrate control and data transmission at the channel capacity of the oscillator, the maximum possible data rate compatible with the grammar.

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PubMed2005

Lag and anticipating synchronization without time-delay coupling.

We describe a new method for achieving approximate lag and anticipating synchronization in unidirectionally coupled chaotic oscillators. The method uses a specific parameter mismatch between the drive and response that is a first-order approximation to true time-delay coupling. As a result, an adjustable lag or anticipation effect can be achieved without the need for a variable delay line, making the method simpler and more economical to implement in many physical systems. We present a stability analysis, demonstrate the method numerically, and report experimental observation of the effect in radio-frequency electronic oscillators. In the circuit experiments, both lag and anticipation are controlled by tuning a single capacitor in the response oscillator.

Models, Statistical↗

PubMed2003

Information flow in chaos synchronization: fundamental tradeoffs in precision, delay, and anticipation.

We use symbolic dynamics to examine the flow of information in unidirectionally coupled chaotic oscillators exhibiting synchronization. The theory of symbolic dynamics reduces chaos to a shift map that acts on a discrete set of symbols, each of which contains information about the system state. Using this transformation we explore so-called achronal synchronization, in which the response lags or leads the drive by a fixed amount of time. We find fundamental tradeoffs between the precision to which the drive state is detected, the quality of synchronization attained, and the delay or anticipation exhibited by the response system. To illustrate these tradeoffs, we provide a physical example using electronic circuits.

Journal Article↗

PubMed2002

Synchronizing the information content of a chaotic map and flow via symbolic dynamics.

In this paper we report an extension to the concept of generalized synchronization for coupling different types of chaotic systems, including maps and flows. This broader viewpoint takes disparate systems to be synchronized if their information content is equivalent. We use symbolic dynamics to quantize the information produced by each system and compare the symbol sequences to establish synchronization. A general architecture is presented for drive-response coupling that detects symbols produced by a chaotic drive oscillator and encodes them in a response system using the methods of chaos control. We include experimental results demonstrating synchronization of information content in an electronic oscillator circuit driven by a logistic map.

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