This paper studies quasi-periodicity phenomena appearing at the transition from spiking to bursting activities in the Pernarowski model of pancreatic beta cells. Continuing the parameter, we show that the torus bifurcation is responsible for the transition between spiking and bursting. Our investigation involves different torus bifurcations, such as supercritical torus bifurcation, saddle torus canard, resonant torus, self-similar torus fractals, and torus destruction. These bifurcations give rise to complex or multistable dynamics. Despite being a dissipative system, the model still exhibits KAM tori, as we have illustrated. We provide two scenarios for the onset of resonant tori using the Poincaré return map, where global bifurcations happen because of the saddle-node or inverse period-doubling bifurcations. The blue-sky catastrophe takes place at the transition route from bursting to spiking.

本文研究了胰腺 β 细胞 Pernarowski 模型中从尖峰活动过渡到爆发活动时出现的准周期性现象。继续参数，我们表明环面分叉负责尖峰和爆发之间的过渡。我们的研究涉及不同的环面分岔，例如超临界环面分岔、鞍环鸭翼、共振环面、自相似环面分形和环面破坏。这些分岔引起复杂或多稳态动力学。尽管是一个耗散系统，该模型仍然表现出 KAM tori，正如我们所说明的。我们使用庞加莱返回图提供了两种共振环面开始的场景，其中由于鞍结点或反倍周期分岔而发生全局分岔。蓝天灾难发生在从爆发到尖峰的过渡路线上。