{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T21:37:08Z","timestamp":1781905028620,"version":"3.54.5"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,5]]},"abstract":"<jats:p> Electrical bursting is an activity which is universal in excitable cells such as neurons and various endocrine cells, and it encodes rich physiological information. As burst delay identifies that the signal integration has reached the threshold at which it can generate an action potential, the number of spikes in a burst may have essential physiological implications, and the transition of bursting in excitable cells is associated with the bifurcation phenomenon closely. In this paper, we focus on the transition of the spike count per burst of the pancreatic [Formula: see text]-cells within a mathematical model and bifurcation phenomenon in the Chay\u2013Keizer model, which is utilized to simulate the pancreatic [Formula: see text]-cells. By the fast\u2013slow dynamical bifurcation analysis and the bi-parameter bifurcation analysis, the local dynamics of the Chay\u2013Keizer system around the Bogdanov\u2013Takens bifurcation is illustrated. Then the variety of the number of spikes per burst is discussed by changing the settings of a single parameter and bi-parameter. Moreover, results on the number of spikes within a burst are summarized in ISIs (interspike intervals) sequence diagrams, maximum and minimum, and the number of spikes under bi-parameter value changes. <\/jats:p>","DOI":"10.1142\/s0218127416500905","type":"journal-article","created":{"date-parts":[[2016,5,31]],"date-time":"2016-05-31T06:25:31Z","timestamp":1464675931000},"page":"1650090","source":"Crossref","is-referenced-by-count":24,"title":["Bifurcation and Spike Adding Transition in Chay\u2013Keizer Model"],"prefix":"10.1142","volume":"26","author":[{"given":"Bo","family":"Lu","sequence":"first","affiliation":[{"name":"School of Mathematics, South China University of Technology, Guangzhou 510640, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shenquan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics, South China University of Technology, Guangzhou 510640, P. R. 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