Excitable Media

Last update: 21 Apr 2025 21:17
First version:

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Mathematical aspects, especially topological arguments. Simulation by cellular automata. Physical and biological realizations (i.e., what makes actual excitable media excitable?). Adaptive roles, if any. Connection to circadian and other biological rhythms. Statistical inference.

See also: Interacting Particle Systems; Nonequilibrium Statistical Mechanics; Pattern Formation; Self-Organization; Slime Molds

Recommended, big picture:
• Arthur Winfree
  • The Geometry of Biological Time
  • When Time Breaks Down

Recommended, close-ups:
• David J. Aidley, The Physiology of Excitable Cells
• H. Busch and F. Kaiser, "Influence of spatiotemporally correlated noise on structure formation in excitable media", Physical Review E 67 (2003): 041105
• Mauro Copelli and Osame Kinouchi, "Intensity Coding in Two-Dimensional Excitable Neural Networks", q-bio.NC/0409032 [Greenberg-Hastings cellular automata as a toy model of visual perception!]
• Fisch, Gravner and Griffeath, "Threshold-range scaling of excitable cellular automata", Statistics and Computing 1 (1991): 23--39 [PDF]
• Fisch, Gravner and Griffeath, "Cyclic Cellular Automata in Two Dimensions", pp. 171--185 in Alexander and Wadkins (eds.), Spatial Stochastic Processes (1991) [zipped PostScript]
• J. Greenberg and S. Hastings, "Spatial Patterns for Discrete Models of Diffusion in Excitable Media", SIAM Journal on Applied Mathematics 34 (1978): 515--523 [JSTOR]
• Satoshi Sawai, Peter A. Thomason and Edward C. Cox, "An autoregulatory circuit for long-range self-organization in Dictyostelium cell populations", Nature 433 (2005): 323--326

To read:
• Daniel S. Calovi, Leonardo G. Brunnet, and Rita M. C. de Almeida, "cAMP diffusion in Dictyostelium discoideum: A Green's function method", Physical Review E 82 (2010): 011909
• Mauro Copelli, Paulo R. A. Campos, "Excitable Scale Free Networks", q-bio.NC/0703004
• Mauro Copelli, Antonio C. Roque, Rodrigo F. Oliveira and Osame Kinouchi, "Enhanced dynamic range in a sensory network of excitable elements," cond-mat/0112395
• Silvina Ponce Dawson, María Verónica D'Angelo and John E. Pearson, "Towards a Global Classification of Exictable Reaction-Diffusion Systems," patt-sol/9811003
• S. de Franciscis, J. J. Torres, and J. Marro, "Unstable dynamics, nonequilibrium phases, and criticality in networked excitable media", Physical Review E 82 (2010): 041105
• Hugo Gil Ferreira and Michael W. Marshall, The Biophysical Basis of Excitability
• Albert Goldbeter, Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behavior
• Arun V. Holden, Mario Markus, and Hans G. Othmer, Nonlinear Wave Processes in Excitable Media
• Hans G. Othmer (ed.), The Dynamics of Excitable Media (22nd symposium on "Some Mathematical Questions in Biology")
• Nita Parekh and Somdatta Sinha, "Controlling Spatiotemporal Dynamics in Excitable Systems," SFI Working Paper 00-06-031
• Y. Zhao, S. A. Billings and Alexander F. Routh, "Identification of Excitable Media Using Cellular Automata Models", International Journal of Bifurcation and Chaos 17 (2007): 153--168