Singular perturbation theory of traveling waves in excitable media (a review)

[1]  Benno Hess,et al.  Curvature and Propagation Velocity of Chemical Waves , 1988, Science.

[2]  James P. Keener,et al.  The dynamics of three-dimensional scroll waves in excitable media , 1988 .

[3]  Meron,et al.  Model for spiral wave formation in excitable media. , 1988, Physical review letters.

[4]  J. Keener,et al.  The Motion of Untwisted Untorted Scroll Waves in Belousov-Zhabotinsky Reagent , 1988, Science.

[5]  James P. Keener,et al.  Dispersion of traveling waves in the Belousov-Zhabotinskii reaction , 1988 .

[6]  Measurement of dispersion relation of chemical waves in an oscillatory reacting medium , 1988 .

[7]  J P Keener.  On the formation of circulating patterns of excitation in anisotropic excitable media , 1988, Journal of mathematical biology.

[8]  P. Grindrod,et al.  Three-dimensional waves in excitable reaction-diffusion systems , 1987 .

[9]  John J. Tyson,et al.  Spiral waves in a model of myocardium , 1987 .

[10]  Arthur T. Winfree,et al.  A computational study of twisted linked scroll waves in excitable media , 1987 .

[11]  A Goldbeter,et al.  A Model Based on Receptor Desensitization for Cyclic AMP Signaling in Dictyostelium Cells. , 1987, Biophysical journal.

[12]  A. V. Panfilopv.  Two regimes of the scroll ring drift in the three-dimensional active media , 1987 .

[13]  J. Tyson,et al.  Luther's 1906 discovery and analysis of chemical waves , 1987 .

[14]  R. Luther.  Propagation of chemical reactions in space , 1987 .

[15]  A. Winfree.  When time breaks down , 1987 .

[16]  Benno Hess,et al.  Two-dimensional spectrophotometry of spiral wave propagation in the Belousov—Zhabotinskii reaction. I. experiments and digital data representation , 1987 .

[17]  B. Hess,et al.  Two-dimensional spectrophotometry of spiral wave propagation in the belousov—Zhabotinskii reaction. II. Geometric and kinematic parameters , 1987 .

[18]  C. Vidal,et al.  Wave profile and speed near the core of a target pattern in the Belousov-Zhabotinsky reaction , 1987 .

[19]  G. Sivashinsky,et al.  On the nonlinear thermal diffusive theory of curved flames , 1987 .

[20]  J. Keener.  A geometrical theory for spiral waves in excitable media , 1986 .

[21]  J. Murray,et al.  On the spatial spread of rabies among foxes , 1986, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[22]  J. Bodet,et al.  Etude expérimentale statistique des structures cibles de la réaction de Belousov-Zhabotinsky en régime oscillant , 1986 .

[23]  P. Ortoleva,et al.  Static reaction-diffusion structures in folded slow manifold systems , 1986 .

[24]  J. Keener,et al.  Spiral waves in the Belousov-Zhabotinskii reaction , 1986 .

[25]  L. Schulman,et al.  Percolation and Galaxies , 1986, Science.

[26]  P. Ortoleva,et al.  Rotating waves in reaction‐diffusion systems with folded slow manifolds , 1986 .

[27]  M. Allessie,et al.  The Wavelength of the Cardiac Impulse and Reentrant Arrhythmias in Isolated Rabbit Atrium: The Role of Heart Rate, Autonomic Transmitters, Temperature, and Potassium , 1986, Circulation research.

[28]  Alexander V. Panfilov,et al.  Turbulent rings in 3-dimensional active media with diffusion by 2 components , 1986 .

[29]  Nancy Kopell,et al.  Coupled Oscillators and Locomotion by Fish , 1986 .

[30]  Alexander V. Panfilov,et al.  Dynamical simulations of twisted scroll rings in three-dimensional excitable media , 1985 .

[31]  B. Hess,et al.  The Structure of the Core of the Spiral Wave in the Belousov-Zhabotinskii Reaction , 1985, Science.

[32]  Irving R. Epstein,et al.  Traveling waves in the nitric acid-iron(II) reaction , 1985 .

[33]  Twisted scroll waves in active three-dimensional media , 1985 .

[34]  J. Ross,et al.  A quantitative study of chemical waves in the Belousov–Zhabotinsky reaction , 1985 .

[35]  R. J. Field,et al.  Stationary concentration patterns in the oregonator model of the Belousov-Zhabotinskii reaction , 1985 .

[36]  E. A. Ermakova,et al.  Rotating spiral waves in a modified Fitz-Hugh-Nagumo model , 1984 .

[37]  Steven H. Strogatz,et al.  Organizing centres for three-dimensional chemical waves , 1984, Nature.

[38]  I. Epstein,et al.  Spatial waves in the reaction of chlorite with iodide , 1984 .

[39]  S. Strogatz,et al.  Singular filaments organize chemical waves in three dimensions IV. Wave taxonomy , 1984 .

[40]  G. Ermentrout,et al.  Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I. , 1984 .

[41]  J. Tyson,et al.  The Speed of Propagation of Oxidizing and Reducing Wave Fronts in the Belousov-Zhabotinskii Reaction , 1984 .

[42]  P. Fife.  Propagator-Controller Systems and Chemical Patterns , 1984 .

[43]  A. Pertsov,et al.  [Vortex ring in a 3-dimensional active medium described by reaction-diffusion equations]. , 1984, Doklady Akademii nauk SSSR.

[44]  A. Mikhailov,et al.  Rotating spiral waves in excitable media: The analytical results , 1983 .

[45]  J Bures,et al.  Spiral waves of spreading depression in the isolated chicken retina. , 1983, Journal of neurobiology.

[46]  Brian J. Welsh,et al.  Three-dimensional chemical waves in the Belousov–Zhabotinskii reaction , 1983, Nature.

[47]  S. Strogatz,et al.  Singular filaments organize chemical waves in three dimensions: I. Geometrically simple waves , 1983 .

[48]  Guy Dewel,et al.  Chemical waves in a two‐dimensional oscillating system , 1983 .

[49]  Rory J. Gowland,et al.  A novel moving boundary reaction involving hydroxylamine and nitric acid , 1983 .

[50]  Patrick S. Hagan,et al.  Spiral Waves in Reaction-Diffusion Equations , 1982 .

[51]  Kenneth Showalter,et al.  Detailed studies of propagating fronts in the iodate oxidation of arsenous acid , 1982 .

[52]  Shinji Koga,et al.  Rotating Spiral Waves in Reaction-Diffusion Systems: Phase Singularities of Multi-Armed Waves , 1982 .

[53]  Nancy Kopell,et al.  Target pattern and spiral solutions to reaction-diffusion equations with more than one space dimension , 1981 .

[54]  P. Hagan,et al.  Target patterns in reaction-diffusion systems , 1981 .

[55]  M. Morad,et al.  A new laser scanning system for measuring action potential propagation in the heart. , 1981, Science.

[56]  P. Devreotes,et al.  Adenosine 3',5'-monophosphate waves in Dictyostelium discoideum: a demonstration by isotope dilution--fluorography. , 1981, Science.

[57]  Nancy Kopell,et al.  Target Patterns and Horseshoes from a Perturbed Central-Force Problem: Some Temporally Periodic Solutions to Reaction-Diffusion Equations , 1981 .

[58]  A. Winfree.  The geometry of biological time , 1991 .

[59]  James P. Keener,et al.  Waves in Excitable Media , 1980 .

[60]  J. Tyson,et al.  Target patterns in a realistic model of the Belousov–Zhabotinskii reaction , 1980 .

[61]  R. W. Joyner,et al.  Simulated propagation of cardiac action potentials. , 1980, Biophysical journal.

[62]  James D. Murray,et al.  Spiral Wave Solutions of Practical Reaction-Diffusion Systems , 1980 .

[63]  J. Buresˇ,et al.  Circulation of cortical spreading depression around electrically stimulated areas and epileptic foci in the neocortex of rats , 1979, Brain Research.

[64]  C. Kahlert,et al.  Winfree Meandering in a 2-Dimensional 2-Variable Excitable Medium , 1979 .

[65]  R. J. Field,et al.  The transition from phase waves to trigger waves in a model of the Zhabotinskii reaction , 1979 .

[66]  R. H. Giles,et al.  The landscape epidemiology of rabies in Virginia. , 1978, The American journal of tropical medicine and hygiene.

[67]  A. Winfree.  Stably Rotating Patterns of Reaction and Diffusion , 1978 .

[68]  M. Dworkin,et al.  Solubility and diffusion coefficient of adenosine 3':5'-monophosphate. , 1977, The Journal of biological chemistry.

[69]  A. Zaikin,et al.  Spatial Effects in Active Chemical Systems. I. Model of Leading Center , 1977 .

[70]  T. Erneux,et al.  Rotating waves as asymptotic solutions of a model chemical reaction , 1977 .

[71]  J. Gross,et al.  Signal emission and signal propagation during early aggregation in Dictyostelium discoideum. , 1976, Journal of cell science.

[72]  Y. Kuramoto,et al.  Pattern Formation in Oscillatory Chemical Reactions , 1976 .

[73]  M. Allessie,et al.  Circus Movement in Rabbit Atrial Muscle as a Mechanism of Tachycardia: II. The Role of Nonuniform Recovery of Excitability in the Occurrence of Unidirectional Block, as Studied with Multiple Microelectrodes , 1976, Circulation research.

[74]  J. Greenberg.  Periodic Solutions to Reaction-Diffusion Equations , 1976 .

[75]  Paul C. Fife,et al.  Pattern formation in reacting and diffusing systems , 1976 .

[76]  J. Ross,et al.  Theory of propagation of discontinuities in kinetic systems with multiple time scales: Fronts, front multiplicity, and pulses , 1975 .

[77]  R. G. Casten,et al.  Perturbation analysis of an approximation to the Hodgkin-Huxley theory , 1975 .

[78]  F. Alcântara,et al.  Signal propagation during aggregation in the slime mould Dictyostelium discoideum. , 1974, Journal of general microbiology.

[79]  J. Ross,et al.  On a variety of wave phenomena in chemical reactions , 1974 .

[80]  Arthur T. Winfree,et al.  Rotating Chemical Reactions , 1974 .

[81]  Richard M. Noyes,et al.  Oscillations in chemical systems. V. Quantitative explanation of band migration in the Belousov-Zhabotinskii reaction , 1974 .

[82]  Arthur T. Winfree,et al.  Wavelike Activity in Biological and Chemical Media , 1974 .

[83]  A. Winfree.  Two kinds of wave in an oscillating chemical solution , 1974 .

[84]  A J Durston,et al.  Dictyostelium discoideum aggregation fields as excitable media. , 1973, Journal of theoretical biology.

[85]  J Rinzel,et al.  Traveling wave solutions of a nerve conduction equation. , 1973, Biophysical journal.

[86]  A. Winfree,et al.  Scroll-Shaped Waves of Chemical Activity in Three Dimensions , 1973, Science.

[87]  A. Zhabotinsky,et al.  Autowave processes in a distributed chemical system. , 1973, Journal of theoretical biology.

[88]  M. Allessie,et al.  Circus Movement in Rabbit Atrial Muscle as a Mechanism of Tachycardia , 1973, Circulation research.

[89]  J. Ross,et al.  Phase waves in oscillatory chemical reactions , 1973 .

[90]  N. Kopell,et al.  Horizontal Bands in the Belousov Reaction , 1973, Science.

[91]  J. L. Hudson,et al.  AN EXPERIMENTAL STUDY OF CHEMICAL WAVE PROPAGATION , 1973 .

[92]  U. F. Franck.  OSCILLATORY BEHAVIOR, EXCITABILITY AND PROPAGATION PHENOMENA ON MEMBRANES AND MEMBRANE-LIKE INTERFACES , 1973 .

[93]  A. Winfree.  Spiral Waves of Chemical Activity , 1972, Science.

[94]  A. Zhabotinsky,et al.  Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System , 1970, Nature.

[95]  T S Nelsen,et al.  Simulation of the electrical and mechanical gradient of the small intestine. , 1968, The American journal of physiology.

[96]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[97]  W. K. Burton,et al.  The growth of crystals and the equilibrium structure of their surfaces , 1951, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[98]  G. H. Markstein,et al.  Experimental and Theoretical Studies of Flame-Front Stability , 1951 .

[99]  R. Fisher.  THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES , 1937 .