Relevant bibliographies by topics / Excitable media

Academic literature on the topic 'Excitable media'

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Published: 4 June 2021
Last updated: 20 February 2023

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Journal articles on the topic "Excitable media"

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Zykov, Vladimir. "Excitable media." Scholarpedia 3, no. 5 (2008): 1834. http://dx.doi.org/10.4249/scholarpedia.1834.

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Colosimo, A. "Theory of excitable media." Journal of Electroanalytical Chemistry and Interfacial Electrochemistry 275, no. 2 (April 1989): 207–8. http://dx.doi.org/10.1016/0022-0728(89)87179-7.

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Colosimo, A. "Theory of Excitable Media." Bioelectrochemistry and Bioenergetics 21, no. 2 (April 1989): 207–8. http://dx.doi.org/10.1016/0302-4598(89)80011-x.

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Andrecut, M. "A Simple Three-States Cellular Automaton for Modelling Excitable Media." International Journal of Modern Physics B 12, no. 05 (February 20, 1998): 601–7. http://dx.doi.org/10.1142/s0217979298000363.

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Wave propagation in excitable media provides an important example of spatiotemporal self-organization. The Belousov–Zhabotinsky (BZ) reaction and the impulse propagation along nerve axons are two well-known examples of this phenomenon. Excitable media have been modelled by continuous partial differential equations and by discrete cellular automata. Here we describe a simple three-states cellular automaton model based on the properties of excitation and recovery that are essential to excitable media. Our model is able to reproduce the dynamics of patterns observed in excitable media.
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Davydov, Davydov, Morozov, Stolyarov, and Yamaguchi. "Autowaves in moving excitable media." Condensed Matter Physics 7, no. 3 (2004): 565. http://dx.doi.org/10.5488/cmp.7.3.565.

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Hagberg, A., and E. Meron. "Propagation failure in excitable media." Physical Review E 57, no. 1 (January 1, 1998): 299–303. http://dx.doi.org/10.1103/physreve.57.299.

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Karamysheva, T. V. "Traveling waves in excitable media." Differential Equations 48, no. 3 (March 2012): 446–48. http://dx.doi.org/10.1134/s0012266112030172.

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Vasiev, Bakthier, Florian Siegert, and Cornelis Weijer. "Multiarmed Spirals in Excitable Media." Physical Review Letters 78, no. 12 (March 24, 1997): 2489–92. http://dx.doi.org/10.1103/physrevlett.78.2489.

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Tóth, Ágota, and Kenneth Showalter. "Logic gates in excitable media." Journal of Chemical Physics 103, no. 6 (August 8, 1995): 2058–66. http://dx.doi.org/10.1063/1.469732.

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Meron, Ehud. "Pattern formation in excitable media." Physics Reports 218, no. 1 (September 1992): 1–66. http://dx.doi.org/10.1016/0370-1573(92)90098-k.

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Dissertations / Theses on the topic "Excitable media"

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Theisen, Bjørn Bjørge. "Waves in Excitable Media." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19373.

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This thesis is dedicated to the study of Barkley's equation, a stiff diffusion-reaction equation describing waves in excitable media. Several numerical solution methods will be derived and studied, range from the simple explicit Euler method to more complex integrating factor schemes. A C++ application with guided user interface created for performing several of the numerical experiments in this thesis will also be described.
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Sailer, Franz-Xaver. "Controlling excitable media with noise." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980114284.

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Armstrong, Gavin Robert. "Chemical waves in excitable media." Thesis, University of Leeds, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427767.

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Courtemanche, Marc. "Reentrant waves in excitable media." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186311.

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This dissertation presents a study of instabilities in the propagation of excitation pulses within spatially-distributed models of cardiac reentry. In one-dimensional closed rings, I study the onset of oscillations in the dynamics of circulating pulses as the ring length is decreased. In two-dimensional sheets, I analyze the spontaneous breakup of rotating spiral waves. In both cases, numerical results illustrating the instability phenomena are obtained using simulations of a partial differential equation (PDE) that models cardiac electrical activity using the Beeler-Reuter (BR) equations. The properties of the PDE model are summarized using the restitution and dispersion curves. The restitution curve gives the dependence of the pulse duration on the recovery time, defined as the elapsed time between the onset of an excitation pulse and the end of the previous excitation pulse. The dispersion curve gives the dependence of the pulse speed on the recovery time. I use these two properties to construct simplified models aimed at capturing the essence of the instabilities observed in the PDE. On the ring, I derive an integral-delay equation for the evolution of the recovery time as a function of the distance along the ring that incorporates the restitution and the dispersion curves. Numerical simulations and bifurcation analysis of the delay equation explain and predict the dynamics of the PDE. In two-dimensions, I extend early work that presented the first clear demonstration of spiral wave breakup in a reasonable discretization of a continuous PDE model of cardiac propagation. Spiral breakup can be observed in the BR model, depending on the value of a parameter controlling the duration of the electrical pulses. I study the appearance of spiral wavebreaks and relate it to the change in restitution properties of the BR equations as the parameter is varied. Finally, the effects of restitution and dispersion in two dimensions are examined in a discrete space/continuous time model of cardiac propagation. Results about the dependence of the propagation speed on the excitation threshold and on the excitation front curvature are obtained analytically. Inclusion of restitution relations derived from the BR equations into this simple model can give rise to spiral wavebreaks.
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Weimar, Jörg Richard. "Cellular automata models for excitable media /." This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-03032009-040651/.

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Weimar, Jörg Richard. "Cellular automata models for excitable media." Thesis, Virginia Tech, 1991. http://hdl.handle.net/10919/41365.

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A cellular automaton is developed for simulating excitable media. First, general "masks" as discrete approximations to the diffusion equation are examined, showing how to calculate the diffusion coefficient from the elements of the mask. The mask is then combined with a thresholding operation to simulate the propagation of waves (shock fronts) in excitable media, showing that (for well-chosen masks) the waves obey a linear "speedcurvature" relation with slope given by the predicted diffusion coefficient. The utility of different masks in terms of computational efficiency and adherence to a linear speed-curvature relation is assessed. Then, a cellular automaton model for wave propagation in reaction diffusion systems is constructed based on these "masks" for the diffusion component and on singular perturbation analysis for the reaction component. The cellular automaton is used to model spiral waves in the Belousov-Zhabotinskii reaction. The behavior of the spiral waves and the movement of the spiral tip are analyzed. By comparing these results to solutions of the Oregonator PDE model, the automaton is shown to be a useful and efficient replacement for the standard numerical solution of the PDE's.


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Beato, Valentina. "Noise-induced pattern formation in excitable media." [S.l.] : [s.n.], 2006. http://opus.kobv.de/tuberlin/volltexte/2007/1419.

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Xu, Jinshan. "Dynamics and synchronization in biological excitable media." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2012. http://tel.archives-ouvertes.fr/tel-00776373.

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This thesis investigates the origin of spontaneous activity in the uterus. This organ does not show any activity until shortly before delivery, where fast and efficient contractions are generated. The aim of this work is to provide insight into the origin of spontaneous oscillations and into the transition from asynchronous to synchronized activity in the pregnant uterus. One intriguing aspect in the uterus is the absence of any pacemaker cell. The organ is composed of muscular cells, which are excitable, and connective cells, whose behavior is purely passive; None of these cells, taken in isolation, spontaneously oscillates. We develop an hypothesis based on the observed strong increase in the electrical coupling between cells in the last days of pregnancy. The study is based on a mathematical model of excitable cells, coupled to each other on a regular lattice, and to a fluctuating number of passive cells, consistent with the known structure of the uterus. The two parameters of the model, the coupling between excitable cells, and between excitable and passive cells, grow during pregnancy.Using both a model based on measured electrophysiological properties, and a generic model of excitable cell, we demonstrate that spontaneous oscillations can appear when increasing the coupling coefficients, ultimately leading to coherent oscillations over the entire tissue. We study the transition towards a coherent regime, both numerically and semi-analytically, using the simple model of excitable cells. Last, we demonstrate that, the realistic model reproduces irregular action potential propagation patterns as well as the bursting behavior, observed in the in-vitro experiments.
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Borek, Bartlomiej. "Dynamics of heterogeneous excitable media with pacemakers." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=107795.

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The heart is a heterogeneous excitable tissue embedded with pacemakers. To understand the fundamental rules governing its behaviour it is useful to investigate the interplay between structure and dynamics in simplified experimental and mathematical models. This thesis examines FitzHugh-Nagumo type reaction-diffusion equation models motivated by experiments with engineered cardiac tissue culture. The aim is to relate how the design properties of these systems determine the underlying spatiotemporal dynamics. First, a functional relation between randomly distributed heterogeneities and conduction velocity is proposed in two dimensional heterogeneous excitable media. The transitions to wave break are studied for two types of heterogeneities related to fibroblasts and collagen deposits. The effects of pacemakers are next considered with a theoretical study of the transitions in one-dimensional wave patterns of a pacemaker reset by a stimulus pulse from a distance. Reflected wave solutions are found near the apparent discontinuity in the phase transition curve of the system, and they grow into more multi-reflected trajectories for a coarser spatial discretization of the model. Finally, the dynamical regimes arising from the interaction of two pacemakers in heterogeneous excitable media are investigated. A novel chick culture is developed to exhibit dominant pacemaker dynamics. This stable rhythm undergoes transitions to more complex reentrant patterns following induction of new pacemakers by the application of the potassium channel blocker, E-4031. The dynamics are reproduced by the FitzHugh-Nagumo model, which further demonstrates the effects of pacemaker size and heterogeneity density on the transition to wave break and reentry. These findings may contribute to our understanding of the generic mechanisms governing the dynamics of wave propagation through heterogeneous excitable media with pacemakers, including healthy and diseased hearts.
Le coeur est un tissu hétérogène excitable qui contient des générateurs de rythme. Pour comprendre les règles fondamentales qui dirigent son comportement, il est utile d'étudier l'interaction entre la structure et la dynamique des modèles expérimentaux et mathématiques simplifiés. Dans cette thèse, j'utilise des modèles d'équations de FitzHugh-Nagumo. Ces modèles sont motivés par l'expérimentation avec des tissus cardiaques modifiés pour étudier comment les propriétés des conceptions influencent la dynamique d'ondes. Tout d'abord, une relation fonctionelle entre la densité des hétérogénéités distribuées au hasard et la vitesse de conduction est proposée dans un modèle numérique de deux dimensions de média hétérogènes excitables. Les transitions à l'onde rupturée sont différentes pour deux types de substrats hétérogènes. Les effets des régions automatiques sont alors considérés avec une étude théorique des transitions dans les ondes unidimensionelles des générateurs de rythme réinitialisés par une seule impulsion d'une distance. Des solutions d'ondes réfléchies se trouvent près de la discontinuité apparente de la courbe de transition de phase du système et deviennent des trajectoires plus complexes pour une discrétisation spatiale plus grossière du modèle. Enfin, les modèles d'ondes résultant de l'interaction de deux générateurs de rythme dans des médias hétérogènes excitables sont étudiés. Une nouvelle culture de tissu cardiaque de poussin est développée pour présenter la dynamique dominante déterminée par un générateur de rythme. Ce rythme stable subit des transitions à des modèles d'ondes réentrants plus complexes suivant l'induction de nouveaux générateurs de rythme, par l'application du bloqueur des canaux potassiques, E-4031. La dynamique est reproduite par le modèle FitzHugh-Nagumo, prévoyant l'effet de la taille du générateur de rythme et la densité de l'hétérogèneité sur la transition de l'onde rupturée et à la réentrée. Ces résultants contribuent à notre compréhension des mécanismes de média hétérogènes excitables avec des générateurs de rythme, dont les coeurs sains et malades.
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Henze, Christopher Ernest. "Vortex filaments in three dimensional excitable media." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186300.

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An "excitable medium", such as nerve fiber or heart tissue, can be locally provoked by a relatively small stimulus to execute a relatively large transient response, followed by recovery to the original rest state. In one-, two-, or three-dimensional excitable media, such episodes of excitation can propagate as nondecrementing pulses, until they are extinguished at the domain boundaries. In two- or three-dimensional excitable media, these travelling wavefronts of excitation can become arranged in self-perpetuating spirals (in 2D) or "scrolls" (in 3D), which rotate indefinitely, organizing the entire medium with periodic wavetrains. In three dimensions, the pivot of the scroll, around which the sheetlike wavefront unfurls, is a one-dimensional space curve, a "vortex filament", which may end only on domain boundaries, or close into rings, and which may be knotted or linked. Vortex filaments and their associated scroll waves are of interest as periodic solutions to the underlying reaction-diffusion equations, and they may also play a role in understanding the behavior of certain natural systems, perhaps most prominently the disintegration of normal coordinated activity in large mammalian hearts known as ventricular fibrillation. Analytic or experimental approaches to investigating vortex filaments have met with limited success, and in any case stand in need of testing. This thesis presents the results of four largescale numerical investigations of vortex filaments, using supercomputers. Starting with various carefully contrived initial conditions, three-dimensional volumes of excitable media are simulated by numerical integration of partial differential equation models. During the run, the form and behavior of the simulated vortex filaments are monitored by means of a "differential geometry toolkit". Emphasis is given to two fronts. First, I tried to establish the existence and properties of stable filament configurations. This resulted in the discovery of half a dozen stable organizing centers, more than doubling the number of previously known periodic solutions. Second, I attempted to discern the factors and rules which govern filament dynamics. This effort is largely guided by and aims to test the so-called "local geometry hypothesis", which supposes that local filament dynamics are determined by local filament geometry.
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Books on the topic "Excitable media"

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F, Pastushenko V., and Chizmadzhev I͡U︡riĭ Aleksandrovich, eds. Theory of excitable media. New York: Wiley, 1987.

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NATO Advanced Research Workshop on Nonlinear Wave Processes in Excitable Media (1989 Leeds, England). Nonlinear wave processes in excitable media. New York: Plenum Press, 1991.

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Holden, Arun V., Mario Markus, and Hans G. Othmer, eds. Nonlinear Wave Processes in Excitable Media. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4899-3683-7.

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Zykov, V. S. Simulation of wave processes in excitable media. Manchester: Manchester University Press, 1987.

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Mantel, Rolf-Martin. Periodic forcing and symmetry breaking of waves in excitable media. [s.l.]: typescript, 1997.

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1943-, Othmer H. G., and National Science Foundation (U.S.), eds. Some mathematical questions in biology: The dynamics of excitable media. Providence, R.I: American Mathematical Society, 1989.

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Currey, Robert Peter. How to use excitable media models in the study and construction of mobile agent systems. Manchester: University of Manchester, 1996.

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Sinha, Sitabhra, and S. Sridhar. Patterns in Excitable Media. CRC Press, 2014. http://dx.doi.org/10.1201/b17821.

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Sridhar, S., and Sitabhra Sinha. Patterns in Excitable Media. Taylor & Francis Group, 2019.

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Othmer, Hans G., Mario Markus, and Arun V. Holden. Nonlinear Wave Processes in Excitable Media. Springer, 2014.

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Book chapters on the topic "Excitable media"

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Mikhailov, Alexander S. "Excitable Media." In Springer Series in Synergetics, 32–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-78556-6_3.

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Mikhailov, Alexander S. "Excitable Media." In Springer Series in Synergetics, 32–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-97269-0_3.

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Winfree, Arthur T. "Excitable Kinetics and Excitable Media." In The Geometry of Biological Time, 258–302. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-3484-3_9.

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Gaylord, Richard J., and Kazume Nishidate. "Contagion in Excitable Media." In Modeling Nature, 155–71. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4684-9405-1_15.

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Courtemanche, Marc, and Alain Vinet. "Reentry in Excitable Media." In Interdisciplinary Applied Mathematics, 191–232. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/978-0-387-21640-9_7.

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Hakim, V. "Spirals in Excitable Media." In Nonlinear PDE’s in Condensed Matter and Reactive Flows, 149–67. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-010-0307-0_7.

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Bressloff, Paul C. "Waves in Excitable Neural Fields." In Waves in Neural Media, 271–318. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8866-8_7.

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Lüneburg, Martin. "Structure Formation in Excitable Media." In Fractals in Biology and Medicine, 266–73. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8501-0_23.

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Müller, Stefan C. "Vortex Formation in Excitable Media." In NATO ASI Series, 333–41. New York, NY: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4684-7847-1_24.

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Keener, James P. "Spiral Waves in Excitable Media." In Lecture Notes in Biomathematics, 115–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-93318-9_7.

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Conference papers on the topic "Excitable media"

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Parlitz, Ulrich. "EXCITABLE MEDIA AND CARDIAC DYNAMICS." In Conferência Brasileira de Dinâmica, Controle e Aplicações. SBMAC, 2011. http://dx.doi.org/10.5540/dincon.2011.001.1.0217.

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Hayase, Yumino. "Self-replicating pulses in excitable media." In Third tohwa university international conference on statistical physics. AIP, 2000. http://dx.doi.org/10.1063/1.1291619.

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Osipov, Grigory V. "SUPPRESSION OF SPATIO-TEMPORAL CHAOS IN EXCITABLE MEDIA." In Proceedings of the IEEE Workshop. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792662_0051.

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Goryachev, Andrei. "Synchronization line defects in oscillatory and excitable media." In Stochastic dynamics and pattern formation in biological systems. AIP, 2000. http://dx.doi.org/10.1063/1.59938.

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Devanand and Jiten C. Kalita. "HOC simulation of Barkley model in excitable media." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON FRONTIERS IN INDUSTRIAL AND APPLIED MATHEMATICS (FIAM-2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5042181.

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Gong, Xiyuan, Tetsuya Asai, and Masato Motomura. "Reaction-diffusion media with excitable oregonators coupled by memristors." In 2012 13th International Workshop on Cellular Nanoscale Networks and their Applications (CNNA 2012). IEEE, 2012. http://dx.doi.org/10.1109/cnna.2012.6331440.

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Zhou, Changsong, Jurgen Kurths, Zoltan Neufeld, and Istvan Z. Kiss. "Noise-sustained oscillation and synchronization of excitable media with stirring." In Second International Symposium on Fluctuations and Noise, edited by Zoltan Gingl. SPIE, 2004. http://dx.doi.org/10.1117/12.546755.

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Senter, James K., D. Wilson, and Amir Sadovnik. "Reinforcement Learning for Elimination of Reentrant Spiral Waves in Excitable Media." In 2020 American Control Conference (ACC). IEEE, 2020. http://dx.doi.org/10.23919/acc45564.2020.9147623.

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Chernihovskyi, Anton, Christian E. Elger, and Klaus Lehnertz. "Analysis of synchronization phenomena in human electroencephalograms with nonlinear excitable media." In 2008 11th International Workshop on Cellular Neural Networks and Their Applications - CNNA 2008. IEEE, 2008. http://dx.doi.org/10.1109/cnna.2008.4588654.

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Zhang, Huan, Guoyong Yuan, Hongling Fan, and Shaoying Chen. "Effect of Two-Part Inhomogeneity on Spiral Wave Dynamics in Excitable Media." In 2011 Fourth International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2011. http://dx.doi.org/10.1109/iwcfta.2011.50.

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