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There exist regions in parameter space in which the neuron is mode locked to the periodic stimulus, and instabilities of the mode locked states lead to an Arnol'd tongue structure in parameter space. We analyze mode locked solutions and examine the bifurcations that define the boundaries of the tongue structures. The theoretical analysis is in excellent agreement with numerical simulations, and this study can be used to further understand the functional features related to responses of such a model neuron to biologically realistic inputs. <\/jats:p>","DOI":"10.1142\/s021812741350171x","type":"journal-article","created":{"date-parts":[[2013,10,30]],"date-time":"2013-10-30T03:12:20Z","timestamp":1383102740000},"page":"1350171","source":"Crossref","is-referenced-by-count":1,"title":["PERIODICALLY FORCED PIECEWISE-LINEAR ADAPTIVE EXPONENTIAL INTEGRATE-AND-FIRE NEURON"],"prefix":"10.1142","volume":"23","author":[{"given":"LIEJUNE","family":"SHIAU","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Houston, Clear Lake, Houston TX 77058, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CARLO R.","family":"LAING","sequence":"additional","affiliation":[{"name":"Institute of Information and Mathematical Sciences, Massey University, Private Bag 102-904, NSMC, Auckland, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,10,29]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.80.051922"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1152\/jn.00686.2005"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1007\/s00422-011-0435-9"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2003.12.009"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2006.10.047"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(99)00172-3"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.60.2086"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.64.041914"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2011.05.012"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1007\/s10827-009-0164-4"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1162\/08997660152002861"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.4249\/scholarpedia.8427"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2007.19.3.706"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1007\/s00422-008-0261-x"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300015277"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1085\/jgp.59.6.767"},{"key":"p_20","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1002478"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405012557"},{"key":"p_22","doi-asserted-by":"crossref","first-page":"1384","DOI":"10.1152\/jn.1992.68.4.1384","volume":"68","author":"McCormick D.","year":"1992","journal-title":"J. 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