scholarly journals Spiral wave in an inhomogeneous excitable medium

2008 ◽  
Vol 57 (11) ◽  
pp. 6815
Author(s):  
Zhang Guo-Yong ◽  
Ma Jun ◽  
Gan Zheng-Ning ◽  
Chen Yong
Keyword(s):  
Spiral Wave ◽  
Excitable Medium

SPIRAL DYNAMICS IN EXCITABLE MEDIUM INDUCED BY EXTERNAL PERIODIC MODULATION

2013 ◽  
Vol 23 (05) ◽  
pp. 1350082
Author(s):  
YU QIAN ◽  
WEI LI ◽  
XIAODONG HUANG ◽  
ZHAOYANG ZHANG ◽  
YUANYUAN MI
Keyword(s):  
Spiral Wave ◽  
Spatiotemporal Dynamics ◽  
Excitable Medium ◽  
Periodic Modulation ◽  
Spiral Dynamics ◽  
External Modulation ◽  
Wave Induced ◽  
Size Variable

Spatiotemporal dynamics of spiral tip and the evolution of spiral wave induced by external periodic modulation has been investigated in a generic excitable model. Tip dynamics of spiral wave depending on the frequency and strength of the external modulation is revealed by the meandering size variable Rx of the tip trajectory. Different effects of frequency and strength on spiral dynamics are observed and the corresponding mechanisms are explained. Finally, we can eliminate spiral wave out of the boundary successfully by suitably choosing the frequency and the strength of the external periodic modulation.

scholarly journals Spiral waves within a bistability parameter region of an excitable medium

2022 ◽  
Author(s):  
Vladimir Zykov ◽  
Eberhard Bodenschatz
Keyword(s):  
Initial Conditions ◽  
Three Dimensional ◽  
Spiral Wave ◽  
Gradient Flow ◽  
Spiral Waves ◽  
Excitable Medium ◽  
Excitable Media ◽  
Circular Trajectory ◽  
Parameter Region ◽  
Scroll Wave

Abstract Spiral waves are a well-known and intensively studied dynamic phenomenon in excitable media of various types. Most studies have considered an excitable medium with a single stable resting state. However, spiral waves can be maintained in an excitable medium with bistability. Our calculations, performed using the widely used Barkley model, clearly show that spiral waves in the bistability region exhibit unique properties. For example, a spiral wave can either rotate around a core that is in an unexcited state, or the tip of the spiral wave describes a circular trajectory located inside an excited region. The boundaries of the parameter regions with positive and "negative" cores have been defined numerically and analytically evaluated. It is also shown that the creation of a positive or "negative" core may depend on the initial conditions, which leads to hysteresis of spiral waves. In addition, the influence of gradient flow on the dynamics of the spiral wave, which is related to the tension of the scroll wave filaments in a three-dimensional medium, is studied.

EXCITABLE SPIRAL WAVES IN NEMATIC LIQUID CRYSTALS

1994 ◽  
Vol 04 (05) ◽  
pp. 1173-1182 ◽  
Author(s):  
P. COULLET ◽  
F. PLAZA
Keyword(s):  
Liquid Crystals ◽  
Electric Field ◽  
Nematic Liquid Crystals ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Excitable Medium ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Excitable System ◽  
Mechanical Analog

A mechanical analog of the chemical and biological excitable medium is proposed. In nematic liquid crystals, the Freedericksz transition induced by a rotating tilted electric field provides a simple example of such a mechanical excitable system. We study this transition, derive a Ginzburg-Landau model for it, and show that the excitable spiral wave can be produced from a retractable finger-like soliton in this context.

Memory in an Excitable Medium: A Mechanism for Spiral Wave Breakup in the Low-Excitability Limit

1999 ◽  
Vol 83 (19) ◽  
pp. 3964-3967 ◽  
Author(s):  
Flavio H. Fenton ◽  
Steven J. Evans ◽  
Harold M. Hastings
Keyword(s):  
Spiral Wave ◽  
Excitable Medium

Complex-Periodic Spiral Waves Induced by Linearly Polarized Electric Field in the Excitable Medium

2019 ◽  
Vol 29 (05) ◽  
pp. 1950071
Author(s):  
Jinming Luo ◽  
Xingyong Zhang ◽  
Jun Tang
Keyword(s):  
Electric Field ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Excitable Medium ◽  
Local Dynamics ◽  
Local Oscillation ◽  
Period 2 ◽  
Defect Line ◽  
Linearly Polarized ◽  
Slow Modulation

Complex-periodic spiral waves are investigated extensively in the oscillatory medium. In this paper, the linearly polarized electric field (LPEF) is employed to induce complex-periodic spiral waves in the excitable medium with abnormal dispersion. As the amplitude of LPEF is increased beyond a threshold, the simple-periodic spiral wave converts into an irregularly complex-periodic one, in which, the local dynamics exhibit several regular spikes followed by one missed spiking period. Furthermore, with the increase of the LPEF amplitude, the missed spiking period follows different numbers of regular spikes [so-called period-1 (P-1), period-2 (P-2), etc.], even a mix of different periods. Meanwhile, the wavelength of the spiral wave transits from a short to a longer one. The pure-periodic (from P-6 to P-2) spirals generally contain defect lines, across which the phase of local oscillation changes by [Formula: see text]. In contrast, there is no defect line in the mixed-periodic spiral waves. This finding indicates that the defect line is not a necessary feature for complex-periodic spiral waves. Moreover, three types of tip trajectories of pure-periodic spiral waves are identified depending on the periods. That is, the outward-petal meandering, the outward-petal meandering with slow modulation, and drifting tip motion, and the tip trajectories could be used to distinguish them from the complex-oscillatory spiral waves.

scholarly journals Efficient control of spiral wave location in an excitable medium with localized heterogeneities

2008 ◽  
Vol 10 (1) ◽  
pp. 015003 ◽  
Author(s):  
J Schlesner ◽  
V S Zykov ◽  
H Brandtstädter ◽  
I Gerdes ◽  
H Engel
Keyword(s):  
Spiral Wave ◽  
Excitable Medium ◽  
Efficient Control

scholarly journals Fast propagation regions cause self-sustained reentry in excitable media

2017 ◽  
Vol 114 (6) ◽  
pp. 1281-1286 ◽  
Author(s):  
Vladimir Zykov ◽  
Alexei Krekhov ◽  
Eberhard Bodenschatz
Keyword(s):  
Spiral Wave ◽  
Spiral Waves ◽  
Excitable Medium ◽  
Excitable Media ◽  
Control Parameters ◽  
Ablation Procedure ◽  
Electrophysiological Activity ◽  
Weakly Conducting ◽  
Rotating Wave ◽  
Theoretical Results

Self-sustained waves of electrophysiological activity can cause arrhythmia in the heart. These reentrant excitations have been associated with spiral waves circulating around either an anatomically defined weakly conducting region or a functionally determined core. Recently, an ablation procedure has been clinically introduced that stops atrial fibrillation of the heart by destroying the electrical activity at the spiral core. This is puzzling because the tissue at the anatomically defined spiral core would already be weakly conducting, and a further decrease should not improve the situation. In the case of a functionally determined core, an ablation procedure should even further stabilize the rotating wave. The efficacy of the procedure thus needs explanation. Here, we show theoretically that fundamentally in any excitable medium a region with a propagation velocity faster than its surrounding can act as a nucleation center for reentry and can anchor an induced spiral wave. Our findings demonstrate a mechanistic underpinning for the recently developed ablation procedure. Our theoretical results are based on a very general and widely used two-component model of an excitable medium. Moreover, the important control parameters used to realize conditions for the discovered phenomena are applicable to quite different multicomponent models.

scholarly journals Spiral-wave dynamics in an excitable medium with many excitability obstacles

2013 ◽  
Vol 62 (16) ◽  
pp. 160502
Author(s):  
Yuan Guo-Yong ◽  
Zhang Huan ◽  
Wang Guang-Rui
Keyword(s):  
Spiral Wave ◽  
Excitable Medium ◽  
Wave Dynamics
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