Using　a　model　of　individual　isolated　pancreatic　beta-cells,　we　investigated　bifurcation　diagrams　of　interspike　intervals　(ISIs)　and　largest　Lyapunov　exponents　(LLE),　which　clearly　demonstrated　a　wide　range　of　transitions　between　different　firing　patterns.　The　numerical　simulation　results　revealed　the　effect　of　different　time　constants　and　ion　channels　on　the　neuronal　discharge　rhythm.　Furthermore,　an　individual　cell　exhibited　tonic　spiking,　square-wave　bursting,　and　tapered　bursting.　Additionally,　several　bifurcation　phenomena　can　be　observed　in　this　paper,　such　as　period-doubling,　period-adding,　inverse　period-doubling　and　inverse　period-adding　scenarios.　In　addition,　we　researched　the　mechanisms　underlying　two　kinds　of　bursting　(tapered　and　square-wave　bursting)　by　use　of　fast-slow　dynamics　analysis.　Finally,　we　analyzed　the　codimension-two　bifurcation　of　the　fast　subsystem　and　studied　cusp　bifurcation,　generalized　Hopf　(or　Bautin)　bifurcation　and　Bogdanov-Takens　bifurcation.