DEFECT-LINE DYNAMICS IN OSCILLATORY SPIRAL WAVES

2006 ◽  
Vol 06 (04) ◽  
pp. L379-L386
Author(s):  
STEVEN WU
Keyword(s):  
Critical Point ◽  
Period Doubling ◽  
Spiral Wave ◽  
Chaotic Regime ◽  
Spiral Waves ◽  
Bifurcation Parameter ◽  
Local Dynamics ◽  
Total Length ◽  
Defect Line ◽  
Large Fluctuations

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.

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 ON BIFURCATIONS OF SPIRAL WAVES IN THE PLANE

1999 ◽  
Vol 09 (08) ◽  
pp. 1501-1516 ◽  
Author(s):  
E. V. NIKOLAEV ◽  
V. N. BIKTASHEV ◽  
A. V. HOLDEN
Keyword(s):  
Period Doubling ◽  
Spiral Wave ◽  
Reaction Diffusion ◽  
Pitchfork Bifurcation ◽  
Spiral Waves ◽  
Model Systems ◽  
Reaction Diffusion Systems ◽  
Double Period ◽  
Diffusion Systems ◽  
Armed Spiral

We describe the simplest bifurcations of spiral waves in reaction–diffusion systems in the plane and present the list of model systems. One-parameter bifurcations of one-armed spiral waves are fold and Hopf bifurcations. Multiarmed spiral waves may additionally undergo a period-doubling pitchfork bifurcation, when two congruent spiral wave solutions, having the "double" period, branch from the original spiral wave at the bifurcation point.

Period doubling and chaotic transient in a model of chain-branching combustion wave propagation

2010 ◽  
Vol 466 (2121) ◽  
pp. 2747-2769 ◽  
Author(s):  
Vladimir Gubernov ◽  
Andrei Kolobov ◽  
Andrei Polezhaev ◽  
Harvinder Sidhu ◽  
Geoffry Mercer
Keyword(s):  
Wave Propagation ◽  
Hopf Bifurcation ◽  
Combustion Wave ◽  
Period Doubling ◽  
Chaotic Regime ◽  
Bifurcation Parameter ◽  
Chain Branching ◽  
Combustion Waves ◽  
Combustion Wave Propagation ◽  
Parameter Values

The propagation of planar combustion waves in an adiabatic model with two-step chain-branching reaction mechanism is investigated. The travelling combustion wave becomes unstable with respect to pulsating perturbations as the critical parameter values for the Hopf bifurcation are crossed in the parameter space. The Hopf bifurcation is demonstrated to be of a supercritical nature and it gives rise to periodic pulsating combustion waves as the neutral stability boundary is crossed. The increase of the ambient temperature is found to have a stabilizing effect on the propagation of the combustion waves. However, it does not qualitatively change the behaviour of the travelling combustion waves. Further increase of the bifurcation parameter leads to the period-doubling bifurcation cascade and a chaotic regime of combustion wave propagation. The chaotic regime has a transient nature and the combustion wave extinguishes when the bifurcation parameter becomes sufficiently large. For Lewis numbers of fuel close to unity, the parameter regions where pulsating solutions exist become very close to each other and this makes it difficult to experimentally observe the period-doubling. It is shown that the average velocity of pulsating waves is less than the speed of the travelling wave for the same parameter values.

scholarly journals Spiral wave unpinning facilitated by wave emitting sites in cardiac monolayers

2019 ◽  
Vol 475 (2230) ◽  
pp. 20190420
Author(s):  
Shreyas Punacha ◽  
Sebastian Berg ◽  
Anupama Sebastian ◽  
Valentin I. Krinski ◽  
Stefan Luther ◽  
...  
Keyword(s):  
Electric Field ◽  
Electrical Activity ◽  
Spiral Wave ◽  
Electrical Stimulus ◽  
Spiral Waves ◽  
Time Interval ◽  
Field Pulse ◽  
The Core ◽  
Rotating Wave ◽  
Multiple Obstacles

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.

scholarly journals Cardiac Spiral Wave Drifting Due to Spatial Temperature Gradients – a Numerical Study

2018 ◽  
Author(s):  
Guy Malki ◽  
Sharon Zlochiver
Keyword(s):  
Numerical Simulations ◽  
Single Cell ◽  
Numerical Study ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Temperature Gradients ◽  
Effect Of Temperature ◽  
Local Perturbation ◽  
Marginal Effect ◽  
Spatial Temperature

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.

"SPIRAL WAVE–TRAVELING CLUSTERING" INTERMITTENCY AND 1/f-NOISE IN A 2D COUPLED MAP LATTICE

1999 ◽  
Vol 09 (05) ◽  
pp. 929-937 ◽  
Author(s):  
MARK A. PUSTOVOIT ◽  
VALERY I. SBITNEV
Keyword(s):  
Probability Density ◽  
Exponential Decay ◽  
Power Law ◽  
Strange Attractor ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Coupled Map Lattice ◽  
The Self ◽  
Saddle Node Bifurcation ◽  
Self Organized

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.

LOCAL ACTIVITY CRITERIA FOR DISCRETE-MAP CNN

2002 ◽  
Vol 12 (06) ◽  
pp. 1227-1272 ◽  
Author(s):  
VALERY I. SBITNEV ◽  
LEON O. CHUA
Keyword(s):  
Logistic Map ◽  
Period Doubling ◽  
Spiral Wave ◽  
Vortex Pinning ◽  
Magnetic Vortex ◽  
Critical Threshold ◽  
Local Activity ◽  
Cell Impedance ◽  
Initial Setting ◽  
Discrete Map

Discrete-time CNN systems are studied in this paper by the application of Chua's local activity principle. These systems are locally active everywhere except for one isolated parameter value. As a result, nonhomogeneous spatiotemporal patterns may be induced by any initial setting of the CNN system when the strength of the system diffusion coupling exceeds a critical threshold. The critical coupling coefficient can be derived from the loaded cell impedance of the CNN system. Three well-known 1D map CNN's (namely, the logistic map CNN, the magnetic vortex pinning map CNN, and the spiral wave reproducing map CNN) are introduced to illustrate the applications of the local activity principle. In addition, we use the cell impedance to demonstrate the period-doubling scenario in the logistic and the magnetic vortex pinning maps.

scholarly journals Predictability of spatio-temporal patterns in a lattice of coupled FitzHugh–Nagumo oscillators

2013 ◽  
Vol 10 (81) ◽  
pp. 20121016 ◽  
Author(s):  
Miriam Grace ◽  
Marc-Thorsten Hütt
Keyword(s):  
Dynamical System ◽  
Spiral Wave ◽  
Temporal Patterns ◽  
Spiral Waves ◽  
Generic Model ◽  
Homogeneous State ◽  
Drift Speed ◽  
Statistical Fluctuations ◽  
Self Organized ◽  
Spatio Temporal

In many biological systems, variability of the components can be expected to outrank statistical fluctuations in the shaping of self-organized patterns. In pioneering work in the late 1990s, it was hypothesized that a drift of cellular parameters (along a ‘developmental path’), together with differences in cell properties (‘desynchronization’ of cells on the developmental path) can establish self-organized spatio-temporal patterns (in their example, spiral waves of cAMP in a colony of Dictyostelium discoideum cells) starting from a homogeneous state. Here, we embed a generic model of an excitable medium, a lattice of diffusively coupled FitzHugh–Nagumo oscillators, into a developmental-path framework. In this minimal model of spiral wave generation, we can now study the predictability of spatio-temporal patterns from cell properties as a function of desynchronization (or ‘spread’) of cells along the developmental path and the drift speed of cell properties on the path. As a function of drift speed and desynchronization, we observe systematically different routes towards fully established patterns, as well as strikingly different correlations between cell properties and pattern features. We show that the predictability of spatio-temporal patterns from cell properties contains important information on the pattern formation process as well as on the underlying dynamical system.

scholarly journals LOCALIZATION OF RESPONSE FUNCTIONS OF SPIRAL WAVES IN THE FITZHUGH–NAGUMO SYSTEM

2006 ◽  
Vol 16 (05) ◽  
pp. 1547-1555 ◽  
Author(s):  
I. V. BIKTASHEVA ◽  
A. V. HOLDEN ◽  
V. N. BIKTASHEV
Keyword(s):  
External Force ◽  
Wave Solution ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Two Dimensional ◽  
Response Functions ◽  
Space And Time ◽  
Wave Drift ◽  
Linearized Problem ◽  
Small Periodic

Dynamics of spiral waves in perturbed, e.g. slightly inhomogeneous or subject to a small periodic external force, two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of the spiral wave drift in space and time are proportional to the forces caused by the perturbation. The forces are defined as a convolution of the perturbation with the spirals Response Functions, which are eigenfunctions of the adjoint linearized problem. In this paper we find numerically the Response Functions of a spiral wave solution in the classic excitable FitzHugh–Nagumo model, and show that they are effectively localized in the vicinity of the spiral core.

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