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

Physica D: Nonlinear Phenomena

Volumn 32, Issue 3, 1988, Pages 327-361

  Tyson, John J ^a   Keener, James P ^b  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 45449123944     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(88)90062-0     Document Type: Article

References (132)

1. Signal propagation during aggregation in the slime mould Dictyostelium discoideum
2. Circus movement in rabbit atrial muscle as a mechanism of tachycardia
3. 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
4. Circus movement in rabbit atrial muscle as a mechanism of tachycardia. III. The "leading circle" concept: a new model of circus movement in cardiac tissue without the involvement of an anatomical obstacle
5. Propagation of chemical reactions in space
6. Traveling waves in the nitric acid-iron (II) reaction
7. Stationary concentration patterns in the Oregonator model of the Belousov-Zhabotinskii reaction
8. The Growth of Crystals and the Equilibrium Structure of their Surfaces
9. The landscape epidemiology of rabies in Virginia
10. Perturbation analysis of an approximation to the Hodgkin-Huxley theory
11. A new laser scanning system for measuring action potential propagation in the heart
12. Dispersion of traveling waves in the Belousov-Zhabotinskii reaction
13. Dictyostelium discoideum aggregation fields as excitable media
14. Spiral wave solutions of practical reaction-diffusion systems
15. Solubility and diffusion coefficient of adenosine 3':5' monophosphate
16. Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I.
17. Rotating waves as asymptotic solutions of a model chemical reaction
18. Oscillations in chemical systems. V. Quantitative explanation of band migration in the Belousov-Zhabotinskii reaction
19. Pattern formation in reacting and diffusing systems
20. Singular perturbation and wave front techniques in reaction-diffusion problems
21. Wave fronts and target patterns
22. Propagator-controller systems and chemical patterns
23. THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES
24. Curvature and propagation velocity of chemical waves
25. Oscillatory behavior, excitability and propagation phenomena on membranes and membrane-like interfaces
26. On the nonlinear thermal diffusive theory of curved flames
27. Urocyon cinereoargenteus
28. Three-dimensional waves in excitable reaction-diffusion systems
29. Spiral waves of spreading depression in the isolated chicken retina
30. A novel moving boundary reaction involving hydroxylamine and nitric acid
31. Periodic solutions to reaction-diffusion equations
32. Signal emission and signal propagation during early aggregation in Dictyostelium discoideum
33. Spiral Waves in Reaction-Diffusion Equations
34. Target patterns in reaction-diffusion systems
35. Detailed studies of propagating fronts in the iodate oxidation of arsenous acid
36. Cytoplasmic clock with same period as division cycle in xenopus eggs
37. A quantitative description of membrane current and its application to conduction and excitation in nerve
38. Waves in Excitable Media
39. A geometrical theory for spiral waves in excitable media
40. On the formation of circulating patterns of excitation in anisotropic excitable media
41. The dynamics of three dimensional scroll waves in excitable media
42. Spiral waves in the Belousov-Zhabotinskii reaction
43. The motion of untwisted untorted scroll waves in Belousov-Zhabotinsky reagent
44. Rotating Spiral Waves in Reaction-Diffusion Systems: Phase Singularities of Multi-Armed Waves
45. A study of the equation of diffusion with increase in the quantity of matter, with application to a biological problem
46. Coupled oscillators and locomotion by fish
47. Horizontal bands in the Belousov reaction
48. Target pattern and spiral solutions to reaction-diffusion equations with more than one space dimension
49. Target patterns and horseshoes from a perturbed central force problem: some temporally periodic solutions to reaction-diffusion equations
50. Circulation of cortical spreading depression around electrically stimulated areas and epileptic foci on the neocortex of rats
51. Pattern Formation in Oscillatory Chemical Reactions
52. II. Sitzung am Dienstag, den 22. Mai, vormittags 9 Uhr, im grossen Auditorium des chemischen Laboratoriums der Technischen Hochschule. Räumliche Fortpflanzung chemischer Reaktionen
53. Stability of periodic traveling wave solutions of a nerve conduction equation
54. A Model Based on Receptor Desensitization for Cyclic AMP Signaling in Dictyostelium Cells
55. Self-organizing structures
56. Experimental and Theoretical Studies of Flame-Front Stability
57. Model for spiral wave formation in excitable media
58. The reverberator in an active meduim: analytical results
59. Rotating spiral waves in excitable media: the analytical results
60. Twisted scroll waves in active three-dimensional media
61. The structure of the core of the spiral wave in the Belousov-Zhabotinskii reaction
62. Two-dimensional spectophotometry and pseudo-color representation of chemical reaction patterns
63. Two-dimensional spectrophotometry of spiral wave propagation in the Belousov-Zhabotinskii reaction
64. Two-dimensional spectrophotometry of spiral wave propagation in the Belousov-Zhabotinskii reaction
65. On the spatial spread of rabies among foxes
66. A computational study of twisted linked scroll waves in excitable media
67. Simulation of the electrical and mechanical gradient of the small intestine
68. Phase waves in oscillatory chemical reactions
69. On a variety of wave phenomena in chemical reactions
70. Theory of propagation of discontinuities in kinetic systems with multiple time scales: front, front multiplicity, and pulses
71. Formation of pulses in an excitable medium
72. Wave profile and speed near the core of a target pattern in the Belousov-Zhabotinsky reaction
73. Measurement of dispersion relation of chemical waves in an oscillatory reaction medium
74. Vortex ring in a three-dimensional active medium described by reaction-diffusion equations
75. Two regimes of scroll ring drift in three-dimensional active media
76. Dynamical simulations of twisted scroll rings in three dimensional excitable media
77. Vortex rings in 3-dimensional active media with diffusion in two components
78. Analytical evaluation of the period of reverberator in an arbitrary model of an active medium
79. Rotating spiral waves in a modified FitzHugh-Nagumo model
80. The transition from phase waves to trigger waves in a model of the Zhabotinskii reaction
81. Traveling wave solutions of a nerve conduction equation
82. Chemical waves
83. Winfree meandering in a 2-dimensional 2-variable excitable medium
84. Propagating reaction-diffusion fronts
85. Percolation and galaxies
86. Simulated propagation of cardiac action potentials
87. Luther's 1906 discovery and analysis of chemical waves
88. The wavelength of cardiac impulse and reentrant arrhythmias in isolated rabbit atrium
89. The relation between discontinuous propagation in anisotropic cardiac muscle and the “vulnerable period” of reentry
90. Rotating waves in reaction-diffusion systems with folded slow manifolds
91. Static reaction-diffusion structures in folded slow manifold systems
92. AN EXPERIMENTAL STUDY OF CHEMICAL WAVE PROPAGATION
93. Adenosine 3',5'-monophosphate waves in Dictyostelium discoideum: a demonstration by isotope dilution-fluorography
94. Phase changes
95. A quantitative account of oscillations, bistability, and traveling waves in the Belousov-Zhabotinskii reaction
96. Singular perturbation theory of target patterns in the Belousov-Zhabotinskii reaction
97. Target patterns in a realistic model of the Belousov-Zhabotinskii reaction
98. Spiral waves in a model of myocardium
99. The speed of propagation of oxidizing and reducing wave fronts in the Belousov-Zhabotinskii reaction
100. Etude expérimentale statisque des structures cibles de la réaction de Belousov-Zhabotinsky en régime oscillant
101. Chemical waves in two-dimensional oscillating system
102. Spatial waves in the reaction of chlorite with iodide
103. Three-dimensional chemical waves in the Belousov-Zhabotinskii reaction
104. A quantitative study of chemical waves in the Belousov–Zhabotinsky reaction
105. Spiral waves of chemical activity
106. Scroll-shaped waves of chemical activity in three dimensional
107. Two kinds of wave in an oscillating chemical solution
108. Rotating Chemical Reactions
109. Wavelike activity in biological and chemical media
110. Stably rotating patterns of reaction and diffusion
111. Singular filaments organize chemical waves in three dimensions: I. Geometrically simple waves
112. Singular filaments organize chemical waves in three dimensions II. Twisted waves
113. Singular filaments organize chemical waves in three dimensions
114. Singular filaments organize chemical waves in three dimensions
115. Organizing centers for three-dimensional chemical waves
116. A model of the leading centre
117. Spatial effects in active chemical systems. I. Model of leading center
118. Concentration wave propagation in two-dimensional liquid-phase self-oscillating system
119. Autowave processes in a distributed chemical system
120. Kinematics of the steady circulation in an excitable medium
121. Analytical evaluation of the dependence of the speed of an excitation wave in a two-dimensional excitable medium on the curvature of its front
122. Kinematics of the non-steady circulation of spiral waves in an excitable medium