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Bifurcation Chaos"],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p> Many types of neurons and excitable cells could intrinsically generate bursting activity, even in an isolated case, which plays a vital role in neuronal signaling and synaptic plasticity. In this paper, we have mainly investigated bursting types and corresponding bifurcations in the pre-B\u00f6tzinger complex respiratory rhythm neuron by using fast\u2013slow dynamical analysis. The numerical simulation results have showed that for some appropriate parameters, the neuron model could exhibit four distinct types of fast\u2013slow bursters. We also explored the bifurcation mechanisms related to these four types of bursters through the analysis of phase plane. Moreover, the first Lyapunov coefficient of the Hopf bifurcation, which can decide whether it is supercritical or subcritical, was calculated with the aid of MAPLE software. In addition, we analyzed the codimension-two bifurcation for equilibria of the whole system and gave a detailed theoretical derivation of the Bogdanov\u2013Takens bifurcation. Finally, we obtained expressions for a fold bifurcation curve, a nondegenerate Hopf bifurcation curve, and a saddle homoclinic bifurcation curve near the Bogdanov\u2013Takens bifurcation point. <\/jats:p>","DOI":"10.1142\/s0218127417500109","type":"journal-article","created":{"date-parts":[[2017,2,10]],"date-time":"2017-02-10T04:42:17Z","timestamp":1486701737000},"page":"1750010","source":"Crossref","is-referenced-by-count":31,"title":["Bursting Types and Bifurcation Analysis in the Pre-B\u00f6tzinger Complex Respiratory Rhythm Neuron"],"prefix":"10.1142","volume":"27","author":[{"given":"Jing","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics, South China University of Technology, Guangzhou 510640, P. R. 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