{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:38:43Z","timestamp":1787236723228,"version":"3.56.0"},"reference-count":42,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p>We propose a novel energy-optimal methodology to synchronize the cells within an excitable medium during spiral wave activity. The optimal stimulus takes the cells of an excitable medium to a target set where the isostables of the system, which measure the time it takes for a given initial condition in phase space to approach a stable fixed point, are diffuse, thereby synchronizing the activity of the medium. This method is illustrated for a FitzHugh--Nagumo-based model which captures important characteristics of the myocardium and represents a significant first step in the development of energy-optimal defibrillation strategies.<\/jats:p>","DOI":"10.1137\/130942851","type":"journal-article","created":{"date-parts":[[2014,6,3]],"date-time":"2014-06-03T15:20:46Z","timestamp":1401808846000},"page":"944-957","source":"Crossref","is-referenced-by-count":11,"title":["An Energy-Optimal Methodology for Synchronization of Excitable Media"],"prefix":"10.1137","volume":"13","author":[{"given":"Dan","family":"Wilson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeff","family":"Moehlis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2014,6,3]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0960-0779(95)00089-5"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/10\/12\/125016"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.96.104101"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1161\/01.CIR.85.5.1865"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-8167.1998.tb01847.x"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1161\/01.CIR.98.15.1517"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1063\/1.1504242"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1161\/CIRCULATIONAHA.108.825091"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(61)86902-6"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1152\/ajpheart.00612.2001"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.84.041927"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.3389\/fphys.2013.00071"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0407860102"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1038\/32164"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1142\/S021812749800190X"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jacc.2012.08.1001"},{"key":"atypb17","unstructured":"D. Kirk,\n                      Optimal Control Theory\n                      , Dover, Mineola, NY, 1998."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.ahj.2003.10.049"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1161\/01.CIR.102.7.748"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1056\/NEJM199909163411203"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1161\/CIRCEP.111.965830"},{"key":"atypb22","first-page":"e46","volume":"121","author":"Lloyd-Jones D.","year":"2009","journal-title":"Circulation"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1038\/nature10216"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1529\/biophysj.106.98160"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2013.06.004"},{"key":"atypb26","unstructured":"I. Mitchell,\n                      A Toolbox of Level Set Methods\n                      , Tech. Report TR-2007-11, University of British Columbia, Vancouver BC, 2007. Available online from http:\/\/www.cs.ubs.ca\/$\\sim$mitchell\/ToolboxLS\/."},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1007\/s10827-012-0419-3"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1161\/01.CIR.99.10.1385"},{"key":"atypb29","unstructured":"L. Pontryagin, K. N. Trirogoff, and L. Neustadt,\n                      The Mathematical Theory of Optimal Processes\n                      , Wiley, New York, 1962."},{"key":"atypb30","unstructured":"W. Press, S. Teukolsky, W. Vetterling, and B. Flannery,\n                      Numerical Recipes: The Art of Scientific Computing\n                      , 3rd ed., Cambridge University Press, New York, 2007."},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1161\/01.CIR.102.14.1664"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1063\/1.166460"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.83.456"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1109\/10.310090"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1056\/NEJM199401273300402"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.86.3678"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2001.0834"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/51\/23\/014"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1016\/S0300-9572(03)00161-8"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1161\/01.RES.0000224540.97431.f0"},{"key":"atypb41","doi-asserted-by":"crossref","unstructured":"A. Winfree,\n                      The Geometry of Biological Time\n                      , Springer, New York, 2001.","DOI":"10.1007\/978-1-4757-3484-3"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.68.026134"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/130942851","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:41:11Z","timestamp":1787233271000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/130942851"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":42,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["10.1137\/130942851"],"URL":"https:\/\/doi.org\/10.1137\/130942851","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]}}}