CHECKERBOARD SPIRAL WAVES IN A 2D COUPLED MAP LATTICE: SCALING EVIDENCE

1999 ◽  
Vol 09 (05) ◽  
pp. 919-928 ◽  
Author(s):  
VALERY I. SBITNEV ◽  
ALEX. O. DUDKIN

Checkerboard spiral waves in a 2D CML under consideration are generic solutions in a narrow parameter layer located adjacent to the saddle-node bifurcation boundary in the spatiotemporal chaos region. The spiral wave self-organization is in close agreement with the Haken's slaving principle. Scaling correspondence between sizes of the spiral waves and the diffusion length that is a natural unit of length in the CML is established.

1998 ◽  
Vol 08 (12) ◽  
pp. 2341-2352 ◽  
Author(s):  
Valery I. Sbitnev

Methods borrowed from nonequilibrium thermodynamics and statistical physics have been employed in the quantitative analysis of spatiotemporal chaos in a 2D coupled map lattice (CML). Emphasis is made on entropy, entropy variation and entropy production. These quantities manifest peculiar changes in a region where spiral waves emerge. The spiral waves observed in the 2D CML are found to be dissipative objects with an elevated entropy production.


1999 ◽  
Vol 09 (05) ◽  
pp. 929-937 ◽  
Author(s):  
MARK A. PUSTOVOIT ◽  
VALERY I. SBITNEV

Intermittency of checkerboard spiral waves and traveling clusterings originating from sudden shrinking of the strange attractor of the 2D CML in the neighborhood of the saddle-node bifurcation boundary is found. A power-law probability density for lifetimes in the spiral wave (laminar) phase is observed, while in the checkerboard clusterings (bursting) phase the above quantity exhibits an exponential decay. This difference can be interpreted through the self-organized behavior of the spiral waves, and the passive relaxation of the disordered checkerboard clusterings.


2009 ◽  
Vol 20 (01) ◽  
pp. 85-96 ◽  
Author(s):  
LIANCHUN YU ◽  
GUOYONG ZHANG ◽  
JUN MA ◽  
YONG CHEN

In this paper, we investigate the possibility to control the spiral waves and spatiotemporal chaos in an excitable media by subthreshold ordered waves, which is by definition in this paper the spatially ordered periodical subthreshold fluctuations of system variables. It is found that both the spiral wave and the spatiotemporal chaos could be driven out of the control domain by perturbation of periodical subthreshold ordered waves. The effective control time declines as the amplitude of subthreshold ordered waves are increased, or their frequencies are decreased. Furthermore, we show that the effectiveness of this method is also dependent on the spatial arrangement of the subthreshold ordered waves. We discuss the possible applications of this method, especially in the control of heart fibrillation.


1997 ◽  
Vol 07 (11) ◽  
pp. 2569-2575 ◽  
Author(s):  
Valery I. Sbitnev

An intermittency of spatiotemporal chaos and checkerboard spiral waves is observed in a 2D coupled sigmoid map lattice. A rotating arm of such a spiral consists of sites oscillating in opposite phases with respect to nearest neighbors. A region of the spiral waves exhibited in the control parameter space is presented. The spatiotemporal intermittency stems from a crisis-induced intermittency of chaotic wanderings and zigzag burstings that is shown in this work.


2006 ◽  
Vol 06 (04) ◽  
pp. L379-L386
Author(s):  
STEVEN WU

We study defect-line dynamics in a 2-D spiral-wave pair in the Rössler model for its underlying local dynamics in period-N and chaotic regimes with a single bifurcation parameter κ. We find that a spiral wave pair is always stable across the period-doubling cascade and in the chaotic regime. When N ≥ 2 defect lines appear spontaneously and a loop exchange occurs across the defect line. There exists a "critical point" κ c below and above which the time-averaged total length of defect lines L converges to almost constant but different values L1 and L2. When κ > κ c defect lines show large fluctuations due to creation and annihilation processes.


Author(s):  
Shreyas Punacha ◽  
Sebastian Berg ◽  
Anupama Sebastian ◽  
Valentin I. Krinski ◽  
Stefan Luther ◽  
...  

Rotating spiral waves of electrical activity in the heart can anchor to unexcitable tissue (an obstacle) and become stable pinned waves. A pinned rotating wave can be unpinned either by a local electrical stimulus applied close to the spiral core, or by an electric field pulse that excites the core of a pinned wave independently of its localization. The wave will be unpinned only when the pulse is delivered inside a narrow time interval called the unpinning window (UW) of the spiral. In experiments with cardiac monolayers, we found that other obstacles situated near the pinning centre of the spiral can facilitate unpinning. In numerical simulations, we found increasing or decreasing of the UW depending on the location, orientation and distance between the pinning centre and an obstacle. Our study indicates that multiple obstacles could contribute to unpinning in experiments with intact hearts.


2018 ◽  
Author(s):  
Guy Malki ◽  
Sharon Zlochiver

ABSTRACTCardiac rotors are believed to be a major driver source of persistent atrial fibrillation (AF), and their spatiotemporal characterization is essential for successful ablation procedures. However, electrograms guided ablation have not been proven to have benefit over empirical ablation thus far, and there is a strong need of improving the localization of cardiac arrhythmogenic targets for ablation. A new approach for characterize rotors is proposed that is based on induced spatial temperature gradients (STGs), and investigated by theoretical study using numerical simulations. We hypothesize that such gradients will cause rotor drifting due to induced spatial heterogeneity in excitability, so that rotors could be driven towards the ablating probe. Numerical simulations were conducted in single cell and 2D atrial models using AF remodeled kinetics. STGs were applied either linearly on the entire tissue or as a small local perturbation, and the major ion channel rate constants were adjusted following Arrhenius equation. In the AF-remodeled single cell, recovery time increased exponentially with decreasing temperatures, despite the marginal effect of temperature on the action potential duration. In 2D models, spiral waves drifted with drifting velocity components affected by both temperature gradient direction and the spiral wave rotation direction. Overall, spiral waves drifted towards the colder tissue region associated with global minimum of excitability. A local perturbation with a temperature of T=28°C was found optimal for spiral wave attraction for the studied conditions. This work provides a preliminary proof-of-concept for a potential prospective technique for rotor attraction. We envision that the insights from this study will be utilize in the future in the design of a new methodology for AF characterization and termination during ablation procedures.


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