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Vadim N. Biktashev - One of the best experts on this subject based on the ideXlab platform.
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Strength-Duration relationship in an Excitable Medium
Communications in Nonlinear Science and Numerical Simulation, 2020Co-Authors: B. Bezekci, Vadim N. BiktashevAbstract:Abstract We consider the strength-duration relationship in one-dimensional spatially extended Excitable media. In a previous study [36] set out to separate initial (or boundary) conditions leading to propagation wave solutions from those leading to decay solutions, an analytical criterion based on an approximation of the (center-)stable manifold of a certain critical solution was presented. The theoretical prediction in the case of strength-extent curve was later on extended to cover a wider class of Excitable systems including multicomponent reaction-diffusion systems, systems with non-self-adjoint linearized operators and in particular, systems with moving critical solutions (critical fronts and critical pulses) [7]. In the present work, we consider extension of the theory to the case of strength-duration curve.
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Scroll wave generation from ischaemic border zone.
2017Co-Authors: Mario Antonioletti, Vadim N. Biktashev, Adrian Jackson, Sanjay R. Kharche, Tomas Stary, Irina V. BiktashevaAbstract:Generation of a scroll wave out of microscopic re-entries in Excitable Medium with random, space- and time-dependent distribution of parameters, modelling movement of ischaemic border zone during reperfusion [69]; Beeler-Reuter [50] kinetics.
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Strength-Duration Relationship in an Excitable Medium
arXiv: Pattern Formation and Solitons, 2016Co-Authors: B. Bezekci, Vadim N. BiktashevAbstract:We consider the strength-duration relationship in one-dimensional spatially extended Excitable media. In a previous study~\cite{idris2008analytical} set out to separate initial (or boundary) conditions leading to propagation wave solutions from those leading to decay solutions, an analytical criterion based on an approximation of the (center-)stable manifold of a certain critical solution was presented. The theoretical prediction in the case of strength-extent curve was later on extended to cover a wider class of Excitable systems including multicomponent reaction-diffusion systems, systems with non-self-adjoint linearized operators and in particular, systems with moving critical solutions (critical fronts and critical pulses) [Bezekci et al., 2015]. In the present work, we consider extension of the theory to the case of strength-duration curve.
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Spatiotemporal irregularity in an Excitable Medium with shear flow.
Physical Review E, 1999Co-Authors: Vadim N. Biktashev, Irina V. Biktasheva, Arun V. Holden, Mikhail A Tsyganov, John Brindley, Nicholas A. HillAbstract:We consider an Excitable Medium moving with relative shear, subjected to a localized disturbance that in a stationary Medium would produce a pair of spiral waves. The spiral waves so created are distorted and then broken by the motion of the Medium. Such breaks generate new spiral waves, and so a "chain reaction" of spiral wave births and deaths is observed. This leads to a complicated spatiotemporal pattern, the "frazzle gas" [term suggested by Markus et al., Nature (London) 371, 402 (1994)], which eventually fills the whole Medium. In this paper, we display and interpret the main features of the pattern.
Ryan G James - One of the best experts on this subject based on the ideXlab platform.
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hidden structures of information transport underlying spiral wave dynamics
Chaos, 2017Co-Authors: Hiroshi Ashikaga, Ryan G JamesAbstract:A spiral wave is a macroscopic dynamics of Excitable media that plays an important role in several distinct systems, including the Belousov-Zhabotinsky reaction, seizures in the brain, and lethal arrhythmia in the heart. Because the spiral wave dynamics can exhibit a wide spectrum of behaviors, its precise quantification can be challenging. Here we present a hybrid geometric and information-theoretic approach to quantifying the spiral wave dynamics. We demonstrate the effectiveness of our approach by applying it to numerical simulations of a two-dimensional Excitable Medium with different numbers and spatial patterns of spiral waves. We show that, by defining the information flow over the Excitable Medium, hidden coherent structures emerge that effectively quantify the information transport underlying the spiral wave dynamics. Most importantly, we find that some coherent structures become more clearly defined over a longer observation period. These findings provide validity with our approach to quantitati...
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hidden structures of information transport underlying spiral wave dynamics
arXiv: Pattern Formation and Solitons, 2016Co-Authors: Hiroshi Ashikaga, Ryan G JamesAbstract:A spiral wave is a macroscopic dynamic of Excitable media that plays an important role in several distinct systems, including the Belousov-Zhabotinsky reaction, seizures in the brain, and lethal arrhythmia in the heart. Because spiral wave dynamics can exhibit a wide spectrum of behaviors, its precise quantification can be challenging. Here we present a hybrid geometric and information-theoretic approach to quantifying spiral wave dynamics. We demonstrate the effectiveness of our approach by applying it to numerical simulations of a two-dimensional Excitable Medium with different numbers and spatial patterns of spiral waves. We show that, by defining information flow over the Excitable Medium, hidden coherent structures emerge that effectively quantify the information transport underlying spiral wave dynamics. Most importantly, we find that some coherent structures become more clearly defined over a longer observation period. These findings validate our approach to quantitatively characterize spiral wave dynamics by focusing on information transport. Our approach is computationally efficient and is applicable to many Excitable media of interest in distinct physical, chemical and biological systems. Our approach could ultimately contribute to an improved therapy of clinical conditions such as seizures and cardiac arrhythmia by identifying potential targets of interventional therapies.
Vicente Pérez-muñuzuri - One of the best experts on this subject based on the ideXlab platform.
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Mixing efficiency in an Excitable Medium with chaotic shear flow.
Physical Review E, 2007Co-Authors: Vicente Pérez-muñuzuri, Guillermo Fernández-garcíaAbstract:The effect of a time-periodic chaotic shear flow on an Excitable chemical Medium is studied numerically. Stirring effects on pattern formation strongly depend on the shear amplitude and the ratio of the advective and chemical time scales (Damkohler number, Da). We have observed that the wave period increases with decreasing Da below some critical value, afterwards the period decreases until complete wave annihilation. In the last case, before final extinction, a set of uncorrelated, nonstationary Excitable dots survive, whose number depends on the mixing rate. Insights on the nature of this critical behavior are obtained through the calculation of the mixing efficiency of the flow.
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Spiral wave meandering induced by fluid convection in an Excitable Medium.
Physical Review E, 2002Co-Authors: V. Pérez-villar, Alejandro Pérez Muñuzuri, M. N. Lorenzo, Vicente Pérez-muñuzuriAbstract:An isothermal reaction-diffusion system is considered in a two-dimensional fluid Medium within a gravitational field. Inhomogeneities in the concentration field of the species give rise to a fluid flow due to buoyancy forces. A two-dimensional reaction-diffusion-convection model of an Excitable Medium is presented. The influence of hydrodynamics on spiral wave dynamics is systematically studied. A kinematic model is also introduced to better understand the mechanisms involved here.
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Super-spiral structures in an Excitable Medium
Nature, 1991Co-Authors: Vicente Pérez-muñuzuri, Rubin R. Aliev, Bakhtier Vasiev, V. Pérez-villar, V. I. KrinskyAbstract:ROTATING spiral waves have been observed in various Excitable media, including heart muscle1, retinae2, cultures of the slime mould Dyctiostelium discoideum3,4 and chemical oscillators such as the Belousov-Zhabotinsky (BZ) reaction5–7. Under certain conditions the spiral wave does not exhibit simple periodic rotation, but quasiperiodic8 (or 'compound'9) rotation, in which the spiral's origin (the tip) meanders10. Recent calculations11 have shown that highly meandering tip motion can impose superstructures on spiral waves. Here we reproduce these patterns experimentally, using the BZ reaction as the Excitable Medium. We induce high tip meander by applying pulses of electrical current locally at the tip12. Image processing of the patterns reveals a spiral wave of larger wavelength superimposed on the original wave, an effect that can be described in terms of a Doppler shift in the original spiral.
Hiroshi Ashikaga - One of the best experts on this subject based on the ideXlab platform.
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hidden structures of information transport underlying spiral wave dynamics
Chaos, 2017Co-Authors: Hiroshi Ashikaga, Ryan G JamesAbstract:A spiral wave is a macroscopic dynamics of Excitable media that plays an important role in several distinct systems, including the Belousov-Zhabotinsky reaction, seizures in the brain, and lethal arrhythmia in the heart. Because the spiral wave dynamics can exhibit a wide spectrum of behaviors, its precise quantification can be challenging. Here we present a hybrid geometric and information-theoretic approach to quantifying the spiral wave dynamics. We demonstrate the effectiveness of our approach by applying it to numerical simulations of a two-dimensional Excitable Medium with different numbers and spatial patterns of spiral waves. We show that, by defining the information flow over the Excitable Medium, hidden coherent structures emerge that effectively quantify the information transport underlying the spiral wave dynamics. Most importantly, we find that some coherent structures become more clearly defined over a longer observation period. These findings provide validity with our approach to quantitati...
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hidden structures of information transport underlying spiral wave dynamics
arXiv: Pattern Formation and Solitons, 2016Co-Authors: Hiroshi Ashikaga, Ryan G JamesAbstract:A spiral wave is a macroscopic dynamic of Excitable media that plays an important role in several distinct systems, including the Belousov-Zhabotinsky reaction, seizures in the brain, and lethal arrhythmia in the heart. Because spiral wave dynamics can exhibit a wide spectrum of behaviors, its precise quantification can be challenging. Here we present a hybrid geometric and information-theoretic approach to quantifying spiral wave dynamics. We demonstrate the effectiveness of our approach by applying it to numerical simulations of a two-dimensional Excitable Medium with different numbers and spatial patterns of spiral waves. We show that, by defining information flow over the Excitable Medium, hidden coherent structures emerge that effectively quantify the information transport underlying spiral wave dynamics. Most importantly, we find that some coherent structures become more clearly defined over a longer observation period. These findings validate our approach to quantitatively characterize spiral wave dynamics by focusing on information transport. Our approach is computationally efficient and is applicable to many Excitable media of interest in distinct physical, chemical and biological systems. Our approach could ultimately contribute to an improved therapy of clinical conditions such as seizures and cardiac arrhythmia by identifying potential targets of interventional therapies.
Alexandre V. Panfilov - One of the best experts on this subject based on the ideXlab platform.
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Formation of fast spirals on heterogeneities of an Excitable Medium.
Physical Review E, 2008Co-Authors: G. B. Makkes Van Der Deijl, Alexandre V. PanfilovAbstract:We study the process of formation of spiral waves in a heterogeneous Excitable Medium under external stimulation, using numerical and analytical methods. We show that in an Excitable Medium with several heterogeneities with respect to refractory period, fast rotating spiral waves can be generated. These fast spirals are formed as a result of a phenomenon of period decrease, which is the generation by a heterogeneity of waves with a period shorter than the period of the external stimulation.
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Scroll waves meandering in a model of an Excitable Medium.
Physical Review E, 2005Co-Authors: Medvinsky, Alexandre V. PanfilovAbstract:We study numerically the dynamics of a scroll wave in a three-dimensional 3D Excitable Medium in the presence of substantial meandering of the corresponding 2D spiral wave in the Aliev-Panfilov model. We identify three types of dynamics of the scroll wave filament—quasi-2D, periodic, and aperiodic meandering— and we study their dependence on parameter settings and thickness of the Medium.
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Scroll breakup in a three-dimensional Excitable Medium.
Physical review. E Statistical physics plasmas fluids and related interdisciplinary topics, 1996Co-Authors: Alexandre V. Panfilov, Paulien HogewegAbstract:We show that a scroll wave in a homogeneous three-dimensional (3D) Excitable Medium can spontaneously break up into an irregular spatial pattern. This occurs in a FitzHugh-Nagumo model with modified dynamics of the slow variable (shortened relative refractory period of the Excitable Medium). The mechanism of the scroll breakup in 3D is similar to the mechanism of the spiral breakup in 2D and is associated with the instability of wave propagation under high frequency forcing. \textcopyright{} 1996 The American Physical Society.
