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Biomedical subjects

Kenneth Showalter

Publications and source records attributed to Kenneth Showalter.

14 recordsLinked to original sources
PubMed2006

Resonance pacemakers in excitable media.

Chemical waves are initiated in an excitable medium by resonance with local periodic forcing of the excitability. Experiments are carried out with a photosensitive Belousov-Zhabotinsky medium, in which the excitability is varied according to the intensity of the imposed illumination. Complex resonance patterns are exhibited as a function of the amplitude and frequency of the forcing. Local resonance-induced wave initiation transforms the medium globally from a quiescent excitable steady state to a periodic state of successive traveling waves.

Journal Article↗
PubMed2006

Spatiotemporal dynamics of networks of excitable nodes.

A network of excitable nodes based on the photosensitive Belousov-Zhabotinsky reaction is studied in experiments and simulations. The addressable medium allows both local and nonlocal links between the nodes. The initial spread of excitation across the network as well as the asymptotic oscillatory behavior are described. Synchronization of the spatiotemporal dynamics occurs by entrainment to high-frequency network pacemakers formed by excitation loops. Analysis of the asymptotic behavior reveals that the dynamics of the network is governed by a subnetwork selected during the initial transient period.

Action Potentials↗
PubMed2005

Spatiotemporal networks in addressable excitable media.

Spatiotemporal networks are studied in a photosensitive Belousov-Zhabotinsky medium that allows both local and nonlocal transmission of excitation. Local transmission occurs via propagating excitation waves, while nonlocal transmission takes place by nondiffusive jumps to destination sites linked to excited sites in the medium. Static, dynamic, and domain link networks are experimentally and computationally characterized. Transitions to synchronized behavior are exhibited with increasing link density, and power-law relations are observed for first-coverage time as a function of link probability.

Gels↗
PubMed2005

Stochastic resonance of electrochemical aperiodic spike trains.

Aperiodic stochastic resonance in an electrochemical system with excitable dynamics is characterized in experiments and simulations. Two different spike trains, one with stochastic and the other with chaotic interspike intervals, are imposed on the system as subthreshold aperiodic signals. Information transmission is quantified by the cross correlation between the subthreshold input signal and the noise induced system response. A maximum is exhibited in the input-output correlation as a function of the noise amplitude. Numerical simulations with an electrochemical model are in excellent agreement with the experimental observations.

Copper Sulfate↗
PubMed2005

Wave front interaction model of stabilized propagating wave segments.

A wave front interaction model is developed to describe the relationship between excitability and the size and shape of stabilized wave segments in a broad class of weakly excitable media. These wave segments of finite size are unstable but can be stabilized by feedback to the medium excitability; they define a separatrix between spiral wave behavior and contracting wave segments. Unbounded wave segments (critical fingers) lie on the asymptote of this separatrix, defining the boundary between excitable and subexcitable media. The model predictions are compared with results from numerical simulations.

Journal Article↗
PubMed2003

Collapse of spatiotemporal chaos.

The transient nature of spatiotemporal chaos is examined in reaction-diffusion systems with coexisting stable states. We find the apparent asymptotic spatiotemporal chaos of the Gray-Scott system to be transient, with the average transient lifetime increasing exponentially with medium size. The collapse of spatiotemporal chaos arises when statistical spatial correlations produce a quasihomogeneous medium, and the system obeys its zero-dimensional dynamics to relax to its stable asymptotic state.

Journal Article↗
PubMed2003

Synchronization of spatiotemporal patterns in locally coupled excitable media.

The synchronization of two distributed Belousov-Zhabotinsky systems is experimentally and theoretically investigated. Symmetric local coupling of the systems is made possible with the use of a video camera-projector scheme. The spatial disorder of the coupled systems, with random initial configurations of spirals, gradually decreases until a final state is attained, which corresponds to a synchronized state with a single spiral in each system. The experimental observations are confirmed with numerical simulations of two identical Oregonator models with symmetric local coupling, and a systematic study reveals generalized synchronization of spiral waves. Several different types of synchronization attractors are distinguished.

Journal Article↗
PubMed2002

Feedback stabilization of unstable propagating waves.

Propagating wave segments are stabilized to a constant size and shape by applying negative feedback from the measured wave area to the excitability of the medium. The locus of steady-state wave size as a function of excitability defines the perturbation threshold for the initiation of spiral waves. This locus also defines the excitability boundary for spiral wave behavior in active media.

Journal Article↗
PubMed2002

Design and control of wave propagation patterns in excitable media.

Intricate patterns of wave propagation are exhibited in a chemical reaction-diffusion system with spatiotemporal feedback. Wave behavior is controlled by feedback-regulated excitability gradients that guide propagation in specified directions. Waves interacting with boundaries and with other waves are observed when interaction terms are incorporated into the control algorithm. Spatiotemporal feedback offers wide flexibility for designing and controlling wave behavior in excitable media.

Journal Article↗
PubMed2001

Topographic organization of Hebbian neural connections by synchronous wave activity.

Experimental studies have revealed that the refinement of early, imprecise connections in the developing visual system involves activity in the retina before the onset of vision. We study the evolution of initially random unidirectional connections between two excitable layers of FitzHugh-Nagumo neurons with simulated spontaneous activity in the input layer. Lateral coupling within the layers yields synchronous neural wave activity that serves as a template for the Hebbian learning process, which establishes topographically precise interlayer connections. (c) 2001 American Institute of Physics.

Journal Article↗
PubMed1998

Formation and evolution of scroll waves in photosensitive excitable media.

Experimental and computational studies of the formation and evolution of scroll waves in three-dimensional excitable media are presented. Scroll waves are initiated in the photosensitive Belousov-Zhabotinsky reaction by perturbing traveling waves transverse to their direction of propagation. Scroll rings are generated by perturbing circular waves, which expand or contract depending on the strength of an imposed excitability gradient and its direction relative to the rotational direction of the scroll wave. (c) 1998 American Institute of Physics.

Journal Article↗
PubMed1997

Nonlinear prediction, filtering, and control of chemical systems from time series.

Prediction, filtering and control of nonlinear systems is formulated in terms of corresponding nonlinear surfaces in the phase space of delayed system readings and control parameters. The construction of these surfaces from time series and their use is demonstrated with a simple chemical model in the chaotic regime. (c) 1997 American Institute of Physics.

Journal Article↗
PubMed1991

Transverse coupling of chemical waves.

The transverse coupling of chemical waves is investigated using a model scheme for excitable media. Chemical waves supported on the surfaces of a semipermeable membrane couple via diffusion through the membrane, resulting in new types of spatiotemporal behavior. The model studies show that spontaneous wave sources may develop from interacting planar waves, giving rise to a complex sequence of patterns accessible only by perturbation. Coupled circular waves result in the spontaneous formation of spiral waves, which subsequently develop patterns in distinct domains with characteristic features. The long time entrainment behavior of coupled spiral waves reveals regions of 1:2 phase locking.

Journal Article↗