{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:50:50Z","timestamp":1753883450035,"version":"3.41.2"},"reference-count":18,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2009,12,13]],"date-time":"2009-12-13T00:00:00Z","timestamp":1260662400000},"content-version":"vor","delay-in-days":346,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>We study Hopf bifurcation solutions to the Monodomain model equipped with FitzHugh\u2010Nagumo cell dynamics. This reaction\u2010diffusion system plays an important role in the field of electrocardiology as a tractable mathematical model of the electrical activity in the human heart. In our setting the (bounded) spatial domain consists of two subdomains: a collection of automatic\ncells surrounded by collections of normal cells. Thus, the cell model features a discontinuous coefficient. Analytical techniques are applied to approximate the time\u2010periodic solution that arises at the Hopf bifurcation point. Accurate numerical experiments are employed to complement our findings.<\/jats:p>","DOI":"10.1155\/2009\/292183","type":"journal-article","created":{"date-parts":[[2009,12,14]],"date-time":"2009-12-14T06:47:05Z","timestamp":1260773225000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh\u2010Nagumo Kinetics"],"prefix":"10.1155","volume":"2009","author":[{"given":"Robert","family":"Artebrant","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2009,12,13]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_6_1_2","DOI":"10.1017\/S0033583506004227"},{"doi-asserted-by":"publisher","key":"e_1_2_6_2_2","DOI":"10.1016\/S0006-3495(61)86902-6"},{"doi-asserted-by":"publisher","key":"e_1_2_6_3_2","DOI":"10.1016\/S0022-5193(89)80200-0"},{"volume-title":"Mathematical Physiology II: Systems Physiology","year":"2008","author":"Keener J.","key":"e_1_2_6_4_2"},{"volume-title":"Computing the Electrical Activity in the Heart","year":"2006","author":"Sundnes J.","key":"e_1_2_6_5_2"},{"volume-title":"Mathematical Physiology","year":"2004","author":"Keener J.","key":"e_1_2_6_6_2"},{"doi-asserted-by":"publisher","key":"e_1_2_6_7_2","DOI":"10.1006\/jtbi.1998.0824"},{"doi-asserted-by":"publisher","key":"e_1_2_6_8_2","DOI":"10.1016\/j.physleta.2006.07.051"},{"doi-asserted-by":"publisher","key":"e_1_2_6_9_2","DOI":"10.1529\/biophysj.105.061820"},{"doi-asserted-by":"publisher","key":"e_1_2_6_10_2","DOI":"10.1016\/j.mbs.2008.04.001"},{"unstructured":"ArtebrantR. TveitoA. andLinesG. T. A method for analyzing the stability of the resting state for a model of pacemaker cells surrounded by stable cells submitted to Mathematical Biosciences and Engineering.","key":"e_1_2_6_11_2"},{"doi-asserted-by":"publisher","key":"e_1_2_6_12_2","DOI":"10.1046\/j.1540-8167.2002.00801.x"},{"volume-title":"Elementary Stability and Bifurcation Theory","year":"1997","author":"Iooss G.","key":"e_1_2_6_13_2"},{"key":"e_1_2_6_14_2","first-page":"363","article-title":"Repetitive activity and Hopf bifurcation under point stimulation for a simple FitzHugh-Nagumo nerve conduction model","volume":"5","author":"Rinzel J.","year":"1978","journal-title":"Journal of Mathematical Biology"},{"doi-asserted-by":"publisher","key":"e_1_2_6_15_2","DOI":"10.1016\/S0006-3495(73)86065-5"},{"doi-asserted-by":"publisher","key":"e_1_2_6_16_2","DOI":"10.1137\/0143058"},{"volume-title":"Applied Functional Analysis","year":"2002","author":"Griffel D. 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