{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T01:35:49Z","timestamp":1777426549086,"version":"3.51.4"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Syst Biol"],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1186\/s12918-017-0422-4","type":"journal-article","created":{"date-parts":[[2017,4,4]],"date-time":"2017-04-04T09:43:52Z","timestamp":1491299032000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Period doubling cascades of limit cycles in cardiac action potential models as precursors to chaotic early Afterdepolarizations"],"prefix":"10.1186","volume":"11","author":[{"given":"Philipp","family":"K\u00fcgler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.A.K.","family":"Bulelzai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andr\u00e9 H.","family":"Erhardt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,4,4]]},"reference":[{"key":"422_CR1","volume-title":"Nonlinear Dynamics and Chaos","author":"SH Strogatz","year":"2015","unstructured":"Strogatz SH. Nonlinear Dynamics and Chaos. Boulder: Westview Press; 2015."},{"issue":"4527","key":"422_CR2","doi-asserted-by":"crossref","first-page":"1350","DOI":"10.1126\/science.7313693","volume":"214","author":"M Guevara","year":"1981","unstructured":"Guevara M, Glass L, Shrier A. Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. Science. 1981; 214(4527):1350\u20131353. doi: 10.1126\/science.7313693 . http:\/\/science.sciencemag.org\/content\/214\/4527\/1350.full.pdf .","journal-title":"Science"},{"key":"422_CR3","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1038\/343653a0","volume":"343","author":"DR Chialvo","year":"1990","unstructured":"Chialvo DR, Gilmour Jr RF, Jalife J. Low dimensional chaos in cardiac tissue. Nature. 1990; 343:653\u20137.","journal-title":"Nature"},{"key":"422_CR4","first-page":"167","volume":"562","author":"MR Guevara","year":"1984","unstructured":"Guevara MR, Ward G, Shrier A, Glass L. Electrical alternans and period-doubling bifurcations. IEEE Comput Cardiol. 1984; 562:167\u201370.","journal-title":"IEEE Comput Cardiol"},{"issue":"9","key":"422_CR5","doi-asserted-by":"crossref","first-page":"2983","DOI":"10.1073\/pnas.0809148106","volume":"106","author":"D Sato","year":"2009","unstructured":"Sato D, Xie LH, Sovari AA, Tran DX, Morita N, Xie F, Karagueuzian H, Garfinkel A, Weiss JN, Qu Z. Synchronization of chaotic early afterdepolarizations in the genesis of cardiac arrhythmias. Proc National Acad Sci. 2009; 106(9):2983\u2013988. doi: 10.1073\/pnas.0809148106 . http:\/\/www.pnas.org\/content\/106\/9\/2983.full.pdf+html .","journal-title":"Proc National Acad Sci"},{"issue":"11 suppl 1","key":"422_CR6","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1161\/CIRCULATIONAHA.112.000570","volume":"128","author":"EG Navarrete","year":"2013","unstructured":"Navarrete EG, Liang P, Lan F, Sanchez-Freire V, Simmons C, Gong T, Sharma A, Burridge PW, Patlolla B, Lee AS, Wu H, Beygui RE, Wu SM, Robbins RC, Bers DM, Wu JC. Screening drug-induced arrhythmia using human induced pluripotent stem cell\u2013derived cardiomyocytes and low-impedance microelectrode arrays. Circulation. 2013; 128(11 suppl 1):3\u201313. doi: 10.1161\/CIRCULATIONAHA.112.000570 .","journal-title":"Circulation"},{"key":"422_CR7","doi-asserted-by":"crossref","first-page":"346","DOI":"10.3389\/fphys.2012.00346","volume":"3","author":"M Hoekstra","year":"2012","unstructured":"Hoekstra M, Mummery C, Wilde A, Bezzina C, Verkerk A. Induced pluripotent stem cell derived cardiomyocytes as models for cardiac arrhythmias. Front Physiol. 2012; 3:346. doi: 10.3389\/fphys.2012.00346 .","journal-title":"Front Physiol"},{"issue":"2","key":"422_CR8","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1111\/j.1476-5381.2012.02118.x","volume":"169","author":"JM Khan","year":"2013","unstructured":"Khan JM, Lyon AR, Harding SE. The case for induced pluripotent stem cell-derived cardiomyocytes in pharmacological screening. British J Pharmacol. 2013; 169(2):304\u201317. doi: 10.1111\/j.1476-5381.2012.02118.x .","journal-title":"British J Pharmacol"},{"issue":"1-2","key":"422_CR9","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s10955-006-9191-y","volume":"128","author":"C Lerma","year":"2007","unstructured":"Lerma C, Krogh-Madsen T, Guevara M, Glass L. Stochastic aspects of cardiac arrhythmias. J Stat Phys. 2007; 128(1-2):347\u201374.","journal-title":"J Stat Phys"},{"issue":"25","key":"422_CR10","doi-asserted-by":"crossref","first-page":"258103","DOI":"10.1103\/PhysRevLett.102.258103","volume":"102","author":"DX Tran","year":"2009","unstructured":"Tran DX, Sato D, Yochelis A, Weiss JN, Garfinkel A, Qu Z. Bifurcation and chaos in a model of cardiac early afterdepolarizations. Phys Rev Lett. 2009; 102(25):258103. doi: 10.1103\/PhysRevLett.102.258103 .","journal-title":"Phys Rev Lett"},{"issue":"6","key":"422_CR11","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.1161\/01.RES.68.6.1501","volume":"68","author":"CH Luo","year":"1991","unstructured":"Luo CH, Rudy Y. A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. Circulation Res. 1991; 68(6):1501\u201326. doi: 10.1161\/01.RES.68.6.1501 . http:\/\/circres.ahajournals.org\/content\/68\/6\/1501.full.pdf+html .","journal-title":"Circulation Res"},{"issue":"3","key":"422_CR12","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1016\/j.bpj.2010.05.019","volume":"99","author":"D Sato","year":"2010","unstructured":"Sato D, Xie LH, Nguyen TP, Weiss JN, Qu Z. Irregularly appearing early afterdepolarizations in cardiac myocytes: Random fluctuations or dynamical chaos?Biophysical J. 2010; 99(3):765\u201373. doi: 10.1016\/j.bpj.2010.05.019 .","journal-title":"Biophysical J"},{"issue":"12","key":"422_CR13","doi-asserted-by":"crossref","first-page":"1891","DOI":"10.1016\/j.hrthm.2010.09.017","volume":"7","author":"JN Weiss","year":"2010","unstructured":"Weiss JN, Garfinkel A, Karagueuzian HS, Chen PS, Qu Z. Early afterdepolarizations and cardiac arrhythmias. Heart Rhythm. 2010; 7(12):1891\u2013899. doi: 10.1016\/j.hrthm.2010.09.017 .","journal-title":"Heart Rhythm"},{"issue":"1","key":"422_CR14","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1093\/cvr\/cvt104","volume":"99","author":"Z Qu","year":"2013","unstructured":"Qu Z, Xie LH, Olcese R, Karagueuzian HS, Chen PS, Garfinkel A, Weiss JN. Early afterdepolarizations in cardiac myocytes: beyond reduced repolarization reserve. Cardiovascular Res. 2013; 99(1):6\u201315. doi: 10.1093\/cvr\/cvt104 . http:\/\/cardiovascres.oxfordjournals.org\/content\/99\/1\/6.full.pdf .","journal-title":"Cardiovascular Res"},{"issue":"1","key":"422_CR15","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1146\/annurev-bioeng-071811-150106","volume":"14","author":"T Krogh-Madsen","year":"2012","unstructured":"Krogh-Madsen T, Christini DJ. Nonlinear dynamics in cardiology. Annu Rev Biomed Eng. 2012; 14(1):179\u2013203. doi: 10.1146\/annurev-bioeng-071811-150106. PMID: 22524390 . http:\/\/dx.doi.org\/10.1146\/annurev-bioeng-071811-150106","journal-title":"Annu Rev Biomed Eng"},{"issue":"3","key":"422_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pone.0151178","volume":"11","author":"P K\u00fcgler","year":"2016","unstructured":"K\u00fcgler P. Early afterdepolarizations with growing amplitudes via delayed subcritical Hopf bifurcations and unstable manifolds of saddle foci in cardiac action potential dynamics. PLoS ONE. 2016; 11(3):1\u201314. doi: 10.1371\/journal.pone.0151178 .","journal-title":"PLoS ONE"},{"issue":"3","key":"422_CR17","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.pbiomolbio.2010.11.001","volume":"105","author":"Z Qu","year":"2011","unstructured":"Qu Z. Chaos in the genesis and maintenance of cardiac arrhythmias. Prog Biophys Mol Biol. 2011; 105(3):247\u201357. doi: 10.1016\/j.pbiomolbio.2010.11.001 . Muscle Excitation-Contraction Coupling: Elements and Integration","journal-title":"Prog Biophys Mol Biol"},{"issue":"6","key":"422_CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pone.0130632","volume":"10","author":"S Zimik","year":"2015","unstructured":"Zimik S, Vandersickel N, Nayak AR, Panfilov AV, Pandit R. A comparative study of early afterdepolarization-mediated fibrillation in two mathematical models for human ventricular cells. PLoS ONE. 2015; 10(6):1\u201320. doi: 10.1371\/journal.pone.0130632 .","journal-title":"PLoS ONE"},{"issue":"5074","key":"422_CR19","doi-asserted-by":"crossref","first-page":"1230","DOI":"10.1126\/science.1519060","volume":"257","author":"A Garfinkel","year":"1992","unstructured":"Garfinkel A, Spano M, Ditto W, Weiss J. Controlling cardiac chaos. Science. 1992; 257(5074):1230\u20131235. doi: 10.1126\/science.1519060 . http:\/\/science.sciencemag.org\/content\/257\/5074\/1230.full.pdf .","journal-title":"Science"},{"issue":"1","key":"422_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1177\/1087057115594589","volume":"21","author":"B Fermini","year":"2016","unstructured":"Fermini B, Hancox JC, Abi-Gerges N, Bridgland-Taylor M, Chaudhary KW, Colatsky T, Correll K, Crumb W, Damiano B, Erdemli G, Gintant G, Imredy J, Koerner J, Kramer J, Levesque P, Li Z, Lindqvist A, Obejero-Paz CA, Rampe D, Sawada K, Strauss DG, Vandenberg JI. A new perspective in the field of cardiac safety testing through the comprehensive in vitro proarrhythmia assay paradigm. J Biomol Screen. 2016; 21(1):1\u201311. doi: 10.1177\/1087057115594589 . http:\/\/jbx.sagepub.com\/content\/21\/1\/1.full.pdf+html .","journal-title":"J Biomol Screen"},{"issue":"2","key":"422_CR21","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1113\/jphysiol.1962.sp006849","volume":"160","author":"D Noble","year":"1962","unstructured":"Noble D. A modification of the Hodgkin\u2013Huxley equations applicable to Purkinje fibre action and pacemaker potentials. J Physiology. 1962; 160(2):317\u201352. doi: 10.1113\/jphysiol.1962.sp006849 .","journal-title":"J Physiology"},{"issue":"20","key":"422_CR22","doi-asserted-by":"crossref","first-page":"3168","DOI":"10.1161\/01.CIR.0000147231.69595.D3","volume":"110","author":"TJ Hund","year":"2004","unstructured":"Hund TJ, Rudy Y. Rate dependence and regulation of action potential and calcium transient in a canine cardiac ventricular cell model. Circulation. 2004; 110(20):3168\u2013174. doi: 10.1161\/01.CIR.0000147231.69595.D3 .","journal-title":"Circulation"},{"issue":"5","key":"422_CR23","doi-asserted-by":"crossref","first-page":"1002061","DOI":"10.1371\/journal.pcbi.1002061","volume":"7","author":"T O\u2019Hara","year":"2011","unstructured":"O\u2019Hara T, Vir\u00e1g L, Varr\u00f3 A, Rudy Y. Simulation of the undiseased human cardiac ventricular action potential: Model formulation and experimental validation. PLoS Comput Biol. 2011; 7(5):1002061. doi: 10.1371\/journal.pcbi.1002061 .","journal-title":"PLoS Comput Biol"},{"issue":"11","key":"422_CR24","doi-asserted-by":"crossref","first-page":"2334","DOI":"10.1007\/s10439-013-0833-3","volume":"41","author":"M Paci","year":"2013","unstructured":"Paci M, Hyttinen J, Aalto-Set\u00e4l\u00e4 K, Severi S. Computational models of ventricular- and atrial-like human induced pluripotent stem cell derived cardiomyocytes. Ann Biomed Eng. 2013; 41(11):2334\u2013348. doi: 10.1007\/s10439-013-0833-3 .","journal-title":"Ann Biomed Eng"},{"issue":"12","key":"422_CR25","doi-asserted-by":"crossref","first-page":"123014","DOI":"10.1088\/0266-5611\/25\/12\/123014","volume":"25","author":"HW Engl","year":"2009","unstructured":"Engl HW, Flamm C, K\u00fcgler P, Lu J, M\u00fcller S, Schuster P. Inverse problems in systems biology. Inverse Problems. 2009; 25(12):123014.","journal-title":"Inverse Problems"},{"issue":"4","key":"422_CR26","doi-asserted-by":"crossref","first-page":"982","DOI":"10.1137\/110834780","volume":"72","author":"P K\u00fcgler","year":"2012","unstructured":"K\u00fcgler P. A sparse update method for solving underdetermined systems of nonlinear equations applied to the manipulation of biological signaling pathways. SIAM J Appl Math. 2012; 72(4):982\u20131001. doi: 10.1137\/110834780 . http:\/\/dx.doi.org\/10.1137\/110834780","journal-title":"SIAM J Appl Math"},{"issue":"6","key":"422_CR27","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.1016\/j.bpj.2013.12.050","volume":"106","author":"Y Xie","year":"2014","unstructured":"Xie Y, Izu LT, Bers DM, Sato D. Arrhythmogenic transient dynamics in cardiac myocytes. Biophys J. 2014; 106(6):1391\u2013397. doi: 10.1016\/j.bpj.2013.12.050 .","journal-title":"Biophys J"},{"key":"422_CR28","volume-title":"Version 8.3.0.532 (R2014a)","author":"MATLAB","year":"2014","unstructured":"MATLAB. Version 8.3.0.532 (R2014a). Natick: The MathWorks Inc.; 2014."},{"key":"422_CR29","volume-title":"Elements of Applied Bifurcation Theory","author":"YA Kuznetsov","year":"2013","unstructured":"Kuznetsov YA, Vol. 112. Elements of Applied Bifurcation Theory. New York: Springer-Verlag; 2013."},{"key":"422_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-1740-9","volume-title":"Practical Bifurcation and Stability Analysis","author":"R Seydel","year":"2010","unstructured":"Seydel R. Practical Bifurcation and Stability Analysis. New York: Springer; 2010."},{"key":"422_CR31","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1145\/779359.779362","volume":"29","author":"A Dhooge","year":"2003","unstructured":"Dhooge A, Govaerts W, Kuznetsov YA. matcont: A matlab package for numerical bifurcation analysis of odes. ACM TOMS. 2003; 29:141\u201364.","journal-title":"ACM TOMS"},{"key":"422_CR32","unstructured":"Doedel EJ, Fairgrieve TF, Sandstede B, Champneys AR, Kuznetsov YA, Wang X. AUTO-07P: Continuation and bifurcation software for ordinary differential equations. 2007."},{"key":"422_CR33","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718195","volume-title":"Simulating, Analyzing and Animating Dynamical Systems","author":"B Ermentrout","year":"2002","unstructured":"Ermentrout B. Simulating, Analyzing and Animating Dynamical Systems. Philadelphia: SIAM; 2002."},{"key":"422_CR34","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-12316-5","volume-title":"Multiple Time Scale Dynamics","author":"C Kuehn","year":"2015","unstructured":"Kuehn C, Vol. 191. Multiple Time Scale Dynamics. New York: Springer; 2015."},{"issue":"2","key":"422_CR35","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1063\/1.166424","volume":"9","author":"R Hegger","year":"1999","unstructured":"Hegger R, Kantz H, Schreiber T. Practical implementation of nonlinear time series methods: The TISEAN package. Chaos: An Interdisciplinary Journal of Nonlinear Science. 1999; 9(2):413\u201335. doi: 10.1063\/1.166424 . http:\/\/dx.doi.org\/10.1063\/1.166424","journal-title":"Chaos: An Interdisciplinary Journal of Nonlinear Science"},{"issue":"8","key":"422_CR36","doi-asserted-by":"crossref","first-page":"1908","DOI":"10.1016\/j.bpj.2015.03.011","volume":"108","author":"Z Song","year":"2015","unstructured":"Song Z, Ko C, Nivala M, Weiss J, Qu Z. Calcium-voltage coupling in the genesis of early and delayed afterdepolarizations in cardiac myocytes. Biophysical J. 2015; 108(8):1908\u2013921. doi: 10.1016\/j.bpj.2015.03.011 .","journal-title":"Biophysical J"},{"issue":"1","key":"422_CR37","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/0167-2789(93)90286-A","volume":"62","author":"XJ Wang","year":"1993","unstructured":"Wang XJ. Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle. Physica D: Nonlinear Phenomena. 1993; 62(1):263\u201374. doi: 10.1016\/0167-2789(93)90286-A .","journal-title":"Physica D: Nonlinear Phenomena"},{"issue":"1","key":"422_CR38","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s11571-011-9184-7","volume":"6","author":"B Jia","year":"2012","unstructured":"Jia B, Gu H, Li L, Zhao X. Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns. Cognitive Neurodynamics. 2012; 6(1):89\u2013106. doi: 10.1007\/s11571-011-9184-7 .","journal-title":"Cognitive Neurodynamics"},{"issue":"1","key":"422_CR39","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1137\/S1111111101394040","volume":"1","author":"J Guckenheimer","year":"2002","unstructured":"Guckenheimer J, Oliva RA. Chaos in the Hodgkin\u2013Huxley model. SIAM J Appl Dyn Syst. 2002; 1(1):105\u201314. doi: 10.1137\/S1111111101394040 . http:\/\/dx.doi.org\/10.1137\/S1111111101394040","journal-title":"SIAM J Appl Dyn Syst"},{"key":"422_CR40","doi-asserted-by":"crossref","first-page":"056214","DOI":"10.1103\/PhysRevE.71.056214","volume":"71","author":"A Shilnikov","year":"2005","unstructured":"Shilnikov A, Calabrese RL, Cymbalyuk G. Mechanism of bistability: Tonic spiking and bursting in a neuron model. Phys Rev E. 2005; 71:056214. doi: 10.1103\/PhysRevE.71.056214 .","journal-title":"Phys Rev E"},{"issue":"1","key":"422_CR41","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.ejps.2008.09.013","volume":"36","author":"T Brennan","year":"2009","unstructured":"Brennan T, Fink M, Rodriguez B. Multiscale modelling of drug-induced effects on cardiac electrophysiological activity. Eur J Pharm Sci. 2009; 36(1):62\u201377. doi: 10.1016\/j.ejps.2008.09.013 .","journal-title":"Eur J Pharm Sci"}],"container-title":["BMC Systems Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s12918-017-0422-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T11:56:33Z","timestamp":1568980593000},"score":1,"resource":{"primary":{"URL":"http:\/\/bmcsystbiol.biomedcentral.com\/articles\/10.1186\/s12918-017-0422-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,4]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["422"],"URL":"https:\/\/doi.org\/10.1186\/s12918-017-0422-4","relation":{},"ISSN":["1752-0509"],"issn-type":[{"value":"1752-0509","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,4,4]]},"article-number":"42"}}