The genesis of period-adding bursting without bursting-chaos in the Chay model

• DOI: 10.1016/j.chaos.2005.04.038
• Publication Date: 2005-06-15T12:03:50Z
• Authors: Zhuoqin Yang; Qishao Lu; Li Li
• Keywords: 0103 physical sciences; 01 natural sciences

Abstract According to the period-adding firing patterns without chaos observed in neuronal experiments, the genesis of the period-adding “fold/homoclinic” bursting sequence without bursting-chaos is explored by numerical simulation, fast/slow dynamics and bifurcation analysis of limit cycle in the neuronal Chay model. It is found that each periodic bursting, from period-1 to period-7, is separately generated by the corresponding periodic spiking pattern through two period-doubling bifurcations, except for the period-1 bursting occurring via a Hopf bifurcation. Consequently, it can be revealed that this period-adding bursting bifurcation without chaos has a compound bifurcation structure with transitions from spiking to bursting, which is closely related to period-doubling bifurcations of periodic spiking in essence.