http://bactra.org/notebooks Cosma's Notebooks en http://bactra.org/notebooks/2009/04/10#excitable-media <P>Mathematical aspects, especially <a href="winding-number.html">topological</a> arguments. Simulation by <a href="cellular-automata.html">cellular automata</a>. Physical and biological realizations (i.e., what makes actual excitable media excitable?). Adaptive roles, if any. Connection to circadian and other biological rhythms. <a href="spatial-statistics.html">Statistical inference</a>. <P>See also: <a href="interacting-particle-systems.html">Interacting Particle Systems</a>; <a href="noneq-sm.html">Nonequilibrium Statistical Mechanics</a>; <a href="pattern-formation.html">Pattern Formation</a>; <a href="self-organization.html">Self-Organization</a>; <a href="slime-molds.html">Slime Molds</a> <ul>Recommended, big picture: <li>Arthur Winfree <ul> <li><cite>The Geometry of Biological Time</cite> <li><cite>When Time Breaks Down</cite> </ul> </ul> <ul>Recommended, close-ups: <li>David J. Aidley, <cite>The Physiology of Excitable Cells</cite> <li>Mauro Copelli and Osame Kinouchi, "Intensity Coding in Two-Dimensional Excitable Neural Networks", <a href="http://arxiv.org/abs/q-bio.NC/0409032">q-bio.NC/0409032</a> [Greenberg-Hastings cellular automata as a toy model of visual perception!] <li>Fisch, Gravner and <a href="http://psoup.math.wisc.edu/">Griffeath</a>, "Threshold-range scaling of excitable cellular automata", <cite>Statistics and Computing</cite> <strong>1</strong> (1991): 23--39 [<a href="http://www.stat.cmu.edu/~cshalizi/462/readings/fgg.pdf">PDF</a>] <li>Fisch, Gravner and Griffeath, "Cyclic Cellular Automata in Two Dimensions", pp. 171--185 in Alexander and Wadkins (eds.), <cite>Spatial Stochastic Processes</cite> (1991) [<a href="http://psoup.math.wisc.edu/papers/cca.zip">zipped PostScript</a>] <li>J. Greenberg and S. Hastings, "Spatial Patterns for Discrete Models of Diffusion in Excitable Media", <cite>SIAM Journal on Applied Mathematics</cite> <strong>34</strong> (1978): 515--523 [<a href="http://www.jstor.org/pss/2100950">JSTOR</a>] <li>Satoshi Sawai, Peter A. Thomason and Edward C. Cox, "An autoregulatory circuit for long-range self-organization in <em>Dictyostelium</em> cell populations", <a href="http://dx.doi.org/10.1038/nature03228"><cite>Nature</cite> <strong>433</strong> (2005): 323--326</a> </ul> <ul>To read: <li>Mauro Copelli, Paulo R. A. Campos, "Excitable Scale Free Networks", <a href="http://arxiv.org/abs/q-bio.NC/0703004">q-bio.NC/0703004</a> <li>Mauro Copelli, Antonio C. Roque, Rodrigo F. Oliveira and Osame Kinouchi, "Enhanced dynamic range in a sensory network of excitable elements," <a href="http://arxiv.org/abs/cond-mat/0112395">cond-mat/0112395</a> <li>Silvina Ponce Dawson, Mar&iacute;a Ver&oacute;nica D'Angelo and John E. Pearson, "Towards a Global Classification of Exictable Reaction-Diffusion Systems," <a href="http://arxiv.org/abs/patt-sol/9811003">patt-sol/9811003</a> <li>Hugo Gil Ferreira and Michael W. Marshall, <cite>The Biophysical Basis of Excitability</cite> <li>Albert Goldbeter, <cite>Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behavior</cite> <li>Arun V. Holden, Mario Markus, and Hans G. Othmer, <cite>Nonlinear Wave Processes in Excitable Media</cite> <li>Hans G. Othmer (ed.), <cite>The Dynamics of Excitable Media</cite> (22nd symposium on "Some Mathematical Questions in Biology") <li>Nita Parekh and Somdatta Sinha, "Controlling Spatiotemporal Dynamics in Excitable Systems," SFI Working Paper 00-06-031 <li>Y. Zhao, S. A. Billings and <a href="http://www.cheng.cam.ac.uk/people/routh.html">Alexander F. Routh</a>, "Identification of Excitable Media Using Cellular Automata Models", <a href="http://dx.doi.org/10.1142/S0218127407017239"><cite>International Journal of Bifurcation and Chaos</cite> <strong>17</strong> (2007): 153--168</a> </ul>