{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:42:58Z","timestamp":1760784178737,"version":"3.37.3"},"reference-count":35,"publisher":"World Scientific Pub Co Pte Ltd","issue":"10","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (CN)","doi-asserted-by":"publisher","award":["11472009"],"award-info":[{"award-number":["11472009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,9]]},"abstract":"<jats:p> The pre-B\u00f6tzinger complex of the mammalian brain stem plays a crucial role in the respiratory rhythms generation. Neurons within the pre-B\u00f6tzinger complex have been found experimentally to yield different firing activities. In this paper, we study the spiking and bursting activities related to the respiratory rhythms in the pre-B\u00f6tzinger complex based on a mathematical model proposed by Butera. Using the one-dimensional first recurrence map induced by dynamics, we investigate the different bursting patterns and their transition of the pre-B\u00f6tzinger complex neurons based on the Butera model, after we derived a one-dimensional map from the dynamical characters of the differential equations, and we obtained conditions for the transition of different bursting patterns. These analytical results were verified through numerical simulations. We conclude that the one-dimensional map contains similar rhythmic patterns as the Butera model and can be used as a simpler modeling tool to study fast\u2013slow models like pre-B\u00f6tzinger complex neural circuit. <\/jats:p>","DOI":"10.1142\/s0218127416501625","type":"journal-article","created":{"date-parts":[[2016,9,23]],"date-time":"2016-09-23T05:53:59Z","timestamp":1474610039000},"page":"1650162","source":"Crossref","is-referenced-by-count":6,"title":["Bursting Transition Dynamics Within the Pre-B\u00f6tzinger Complex"],"prefix":"10.1142","volume":"26","author":[{"given":"Lixia","family":"Duan","sequence":"first","affiliation":[{"name":"College of Science, North China University of Technology, Beijing 100144, P. R. China"}]},{"given":"Xi","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Science, North China University of Technology, Beijing 100144, P. R. China"}]},{"given":"Xuhui","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Science, North China University of Technology, Beijing 100144, P. R. China"}]},{"given":"Jianzhong","family":"Su","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA"}]}],"member":"219","published-online":{"date-parts":[[2016,9,23]]},"reference":[{"key":"S0218127416501625BIB001","doi-asserted-by":"publisher","DOI":"10.1137\/0149003"},{"key":"S0218127416501625BIB002","doi-asserted-by":"publisher","DOI":"10.1137\/050625540"},{"key":"S0218127416501625BIB003","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1152\/jn.1999.82.1.382","volume":"82","author":"Butera R. J.","year":"1999","journal-title":"J. Neurophysiol."},{"key":"S0218127416501625BIB004","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1152\/jn.1999.82.1.398","volume":"82","author":"Butera R. 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