A Coupled-Map Lattice for Simulating Waves in Excitable Media

The identification problem for excitable media is investigated in this paper. A new scalar coupled map lattice (SCML) model is introduced and the orthogonal least squares algorithm is employed to determinate the structure of the SCML model and to estimate the associated parameters. A simulated pattern and a pattern observed directly from a real Belousov–Zhabotinsky reaction are identified. The identified SCML models are shown to possess almost the same local dynamics as the original systems and are able to provide good long term predictions.

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A SIMPLE SCALAR COUPLED MAP LATTICE MODEL FOR EXCITABLE MEDIA

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127411030520 ◽

2011 ◽

Vol 21 (11) ◽

pp. 3277-3292 ◽

Cited By ~ 3

Author(s):

YUZHU GUO ◽

YIFAN ZHAO ◽

DANIEL COCA ◽

S. A. BILLINGS

Keyword(s):

Lattice Model ◽

Simple Structure ◽

Coupled Map Lattice ◽

Spatiotemporal Patterns ◽

Excitable Media ◽

New Model

A simple scalar coupled map lattice (sCML) model for excitable media is derived in this paper. The new model, which has a simple structure, is shown to be closely related to the observed phenomena in excitable media. Properties of the sCML model are also investigated. Illustrative examples show that this kind of model is capable of reproducing the behavior of excitable media and of generating complex spatiotemporal patterns.

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Entrainment and Annihilation of Reentrant Excitation in a Periodically Stimulated Ring of Excitable Media

Methods of Information in Medicine ◽

10.1055/s-0038-1636861 ◽

1997 ◽

Vol 36 (04/05) ◽

pp. 290-293

Author(s):

L. Glass ◽

T. Nomura

Keyword(s):

Cardiac Arrhythmias ◽

Initial Phase ◽

Human Heart ◽

Periodic Wave ◽

Excitable Media ◽

One Dimensional ◽

Clinical Observations ◽

Periodic Stimulation ◽

Reentrant Excitation ◽

Stimulation Of

Abstract:Excitable media, such as nerve, heart and the Belousov-Zhabo- tinsky reaction, exhibit a large excursion from equilibrium in response to a small but finite perturbation. Assuming a one-dimensional ring geometry of sufficient length, excitable media support a periodic wave of circulation. As in the periodic stimulation of oscillations in ordinary differential equations, the effects of periodic stimuli of the periodically circulating wave can be described by a one-dimensional Poincaré map. Depending on the period and intensity of the stimulus as well as its initial phase, either entrainment or termination of the original circulating wave is observed. These phenomena are directly related to clinical observations concerning periodic stimulation of a class of cardiac arrhythmias caused by reentrant wave propagation in the human heart.

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Feedback control of wave propagation patterns in excitable media

10.33915/etd.1846 ◽

2003 ◽

Author(s):

Florin Chirila

Keyword(s):

Wave Propagation ◽

Feedback Control ◽

Excitable Media

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High-sensitivity image encryption algorithm with random cross diffusion based on dynamically random coupled map lattice model

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2020.110582 ◽

2021 ◽

Vol 143 ◽

pp. 110582

Author(s):

Xingyuan Wang ◽

Jingjing Yang ◽

Nana Guan

Keyword(s):

Image Encryption ◽

Lattice Model ◽

High Sensitivity ◽

Coupled Map Lattice ◽

Encryption Algorithm ◽

Cross Diffusion ◽

Image Encryption Algorithm

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Evolutionary-based image encryption using biomolecules and non-coupled map lattice

Optics & Laser Technology ◽

10.1016/j.optlastec.2021.106974 ◽

2021 ◽

Vol 140 ◽

pp. 106974

Author(s):

Ali Asghar Abbasi ◽

Mahdi Mazinani ◽

Rahil Hosseini

Keyword(s):

Image Encryption ◽

Coupled Map Lattice

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Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization

Journal of The Royal Society Interface ◽

10.1098/rsif.2014.0352 ◽

2014 ◽

Vol 11 (97) ◽

pp. 20140352 ◽

Cited By ~ 99

Author(s):

Alfonso Bueno-Orovio ◽

David Kay ◽

Vicente Grau ◽

Blanca Rodriguez ◽

Kevin Burrage

Keyword(s):

Structural Heterogeneity ◽

Biological Tissues ◽

Tissue Level ◽

Fractional Diffusion ◽

Diffusion Models ◽

Excitable Media ◽

Research Fields ◽

Dispersion Of Repolarization ◽

Electrical Propagation

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

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