Varieties of spiral wave behavior: An experimentalist's approach to the theory of excitable media

Chaos

Volumn 1, Issue 3, 1991, Pages 303-334

  Winfree, Arthur T ^a  

^a UNIVERSITY OF ARIZONA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749361692     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.165844     Document Type: Article

References (132)

1. Dynamics of Spiral Waves in Non-equilibrium Media
2. Target and Spiral Waves in Oscillatory Media in the Presence of Obstacles
3. Several Modes of Excitation Movement in Ideal Excitable Tissue
4. A Model for Fast Computer Simulation of Waves in Excitable Media
5. Spiral Wave Dynamics in a Simple Model of Excitable Media: Transition from Simple to Compound Rotation
6. Diffusion of Autowaves
7. Vortex Rings in Distributed Excitable Media
8. Perturbation Analysis of an Approximation to the Hodgkin-Huxley Theory
9. Rotating Spiral Wave Solutions of Reaction-Diffusion Equations
10. Defect-mediated Turbulence
11. Stable Three-dimensional Action Potential Circulation in the FitzHugh-Nagumo Model
12. Re-entrant Rotating Waves in a Beeler-Reuter Based Model of Two-dimensional Cardiac Conduction
13. Kinematical Theory of Autowave Patterns in Excitable Media
14. Influence of Anisotropic Tissue Structure on Reentrant Circuits in the Epicardial Border Zone of Subacute Canine Infarcts
15. Diffusive Effects on Dispersion in Excitable Media
16. Dispersion of Traveling Waves in the Belousov-Zhabotinskii Reaction
17. Spiral Wave Solutions of Practical Reaction-Diffusion Systems
18. Impulse Patterning and Relaxational Propagation in Excitable Media
19. Stability of Vortex Rotation in Excitable Cellular Media
20. Transition from Circular to Linear Rotation of a Vortex in an Excitable Cellular Medium
21. Propagator-Controller Systems and Chemical Patterns
22. Understanding the Patterns in the BZ Reagent
23. Dynamics of Internal Layers and Diffusive Interfaces
24. Impulses and Physiological States in Theoretical Models of Nerve Membrane
25. Mathematical Models of Excitation and Propagation in Nerve
26. Curvature and Spiral Geometry in Aggregation Patterns of Dictyostelium discoideum
27. Structures and Spatio-Temporal Chaos in Nonequilibrium Media
28. A Cellular Automaton Model of Excitable Media Including the Effects of Curvature., and Dispersion
29. A Cellular Automaton Model of Excitable Media II. Curvature, Dispersion, Rotating Waves and Meandering Waves
30. A Cellular Automaton Model of Excitable Media III. Fitting the Belousov-Zhabotinsky Reaction
31. A Cellular Automaton Model of Excitable Media IV. Untwisted Scroll Rings
32. Interactions and Dynamics of Topological Defects: Theory and Experiments near the Onset of Weak Turbulence
33. Mechanism of the Formation of Closed Pathways of Conduction in Excitable Media (in Russian)
34. A Stable Knotted Singularity in an Excitable Medium
35. Stable Helical Organizing Centers in Excitable Media
36. Analytical Models of Propagation in Excitable Cells
37. Spiral Breakup in a New Model of Discrete Excitable Media
38. Chemical Vortex Dynamics in Three-dimensional Excitable Media
39. Chemical Vortex Dynamics in the Belousov-Zhabotinsky Reaction and in the 2-Variable Oregonator Model
40. A Survey of Spiral Wave Behavior in the Oregonator Model
41. Spatiotemporal Concentration Patterns in a Surface Reaction: Propagating and Standing Waves, Rotating Spirals, and Turbulence
42. Effects of Tissue Geometry on Initiation of a Cardiac Action Potential
43. Discrete Models for Chemically Reacting Systems
44. Meandering Transition in Two-dimensional Excitable Media
45. Universal Limit of Spiral Wave Propagation in Excitable Media
46. Waves in Excitable Media
47. A Geometrical Theory for Spiral Waves in Excitable Media
48. Spiral Waves in the Belousov-Zhabotinsky Reaction
49. Effect of Diffusion on Patterns in Excitable Belousov-Zhabotinsky Systems
50. Effect of the Parameters and Properties of an Excitable Medium on the Process of Fibrillation
51. Circulation of an Impulse in an Excitable Medium. Critical Size of a Closed Circuit
52. Steady Speeds of Spread of the Stable and Unstable Impulses: Dependence on Ionic Currents of the Membrane
53. Rotating Spiral Waves in Reaction-Diffusion Systems: Phase Singularities of Multi-Armed Waves
54. Schrödinger Equation Approach to Rotating Spiral Waves in Reaction-Diffusion Systems
55. The Simplified FitzHugh-Nagumo Model with Slow Recovery Properties and 2-D Wave Propagation
56. Target Pattern and Spiral Solutions to Reaction-Diffusion Equations with More Than One Space Dimension
57. Mathematical Models of Cardiac Arrhythmias (Spiral Waves)
58. Quasi-Harmonic Rotating Waves in Distributed Active Systems
59. Investigation of One Mechanism of Origin of the Ectopic Focus of Excitation in Modified Hodgkin-Huxley Equations (in Russian)
60. Spiral Calcium Wave Propagation and Annihilation
61. Analysis of Meandering in Zykov-Kinetics
62. Simulation of Wave Propagation in Three Dimensions using Fortran on the Cyber 205
63. Spiral and Concentric Waves in Active Media with Hard and Soft Excitation
64. Scaling Uniform Rotors in the Singular Perturbation Limit
65. Model for Spiral Wave Formation in Excitable Media
66. The Role of Curvature and Wavefront Interactions in Spiral Wave Dynamics
67. Rotating Spiral Waves in Excitable Media: The Analytic Results
68. Kinematical Theory of Spiral Waves in Excitable Media: Comparison with Numerical Simulations
69. Self-generation of Turbulent Vortices in a Two-dimensional Model of Cardiac Tissue
70. Spatio-temporal Chaos in a Model of Cardiac Electrical Activity
71. Two Regimes of the Scroll Ring Drift in Three-dimensional Active Media
72. Wavefront Interaction in Steadily Rotating Spirals
73. The Relationship of Excitability to Conduction Velocity in Canine Purkinje Tissue
74. Instabilities of Autowaves in Excitable Media Associated with Critical Curvature Phenomena
75. Rotating Spiral Waves in a Modified FitzHugh-Nagumo Model
76. Spiral Wave Dynamics as a Function of Proton Concentration in the Ferroin-catalyzed Belousov-Zhabotinsky Reaction
77. Spatial Stability of Traveling Wave Solutions of a Nerve Conduction Equation
78. Traveling Wave Solutions of a Nerve Conduction Equation
79. Winfree Meandering in a 2-Dimensional 2-Variable Excitable Medium
80. Imaging of Spatio-temporal Pattern Evolution during Carbon Monoxide Oxidation on Platinum
81. Spiral Waves in a Model of the Ferroin Catalyzed Belousov-Zhabotinsky Reaction
82. Desynchronization in a Self-Oscillating Medium
83. Numerical Study of Vortex Motion in the Two Dimensional Ginzburg-Landau Equation
84. Luther’s 1906 Discovery and Analysis of Chemical Waves
85. Stable Vortex Rings of Excitation in Neuroelectric Media
86. Symmetry Reduction for the Three-dimensional Landau-Ginzburg Equation
87. Analysis of the Three-dimensional Time-dependent Landau-Ginzburg Equation and its Solutions
88. Periodic to Quasiperiodic Transition of Chemical Spiral Rotation
89. Anisotropic Conduction Properties of Canine Ventricular Muscles
90. Target Patterns in a Realistic Model of the Belousov-Zhabotinskii Reaction
91. Spiral Waves in a Model of Myocardium
92. Singular Perturbation Theory of Traveling Waves in Excitable Media
93. Cyclic-AMP Waves during Aggregation of Dictyostelium Amoebae
94. Computer Simulation of Arrhythmias in a Network of Coupled Excitable Elements
95. A Trial Phase Function Method for a Class of Lambda-Omega Reaction-Diffusion Systems: Reduction to a Schrodinger Type Problem in an Eigen Sub-Domain
96. Scroll-shaped Waves of Chemical Activity in Three Dimensions
97. Rotating Chemical Reactions
98. Wavelike Activity in Biological and Chemical Media
99. Stably Rotating Patterns of Reaction and Diffusion
100. Electrical Instability in Cardiac Muscle: Phase Singularities and Rotors
101. Ventricular Reentry in Three Dimensions
102. Discrete Spectrum of Rotor Periods in an Excitable Medium
103. Multiple Stable Solutions to the Kinetic Equations of an Excitable Medium
104. Alternative Stable Rotors in an Excitable Medium
105. Vortices in Motionless Media
106. Estimating the Ventricular Fibrillation Threshold
107. Three-dimensional Scroll Ring Dynamics in the Belousov-Zhabotinsky Reagent and in the 2-variable Oregonator Model
108. Anisotropic Reentry in the Epicardial Border Zone of Myocardial Infarcts
109. Topological Invariants and Strings in Distributed Active Dynamical Systems
110. Cycloidal Circulation of Spiral Waves in an Excitable Medium
111. Computer Simulation and Investigation of Spiral Autowave Stability