Ghostburster模型鞍结分岔点附近放电模式的转迁控制

Controlling the Firing Patterns Around a Saddle-Node Bifurcation in the Ghostburster Model

在不同的电流刺激下,ghostburster模型表现出周期放电、混沌簇放电、周期簇放电等多种放电模式.其中,周期放电和混沌簇放电之间的转迁是通过极限环的鞍结分岔实现的.应用washout滤波器实现了ghostburster模型鞍结分岔点周围放电模式的转迁;并通过快慢系统分解方法分析了放电模式转迁的内在机制.研究发现快子系统固定点的鞍结分岔和快子系统从周期一极限环转换到周期二极限环的临界点在树突产生不完全放电过程中起到关键作用.Washout滤波器的加入改变了树突膜电位极大值的分岔点的位置,从而改变了ghostburster模型的放电模式.

The ghostburster model exhibits periodic spiking, chaotic bursting and periodic bursting responding to different depolarized currents. The transition between periodic spiking and chaotic bursting is caused by the saddle- node bifurcation of limit cycles. The transition of neuronal dynamics near the saddle-node bifurcation point of limit cycles was realized by a washout filter-aid feedback approach, and the intrinsic mechanisms of these transitions were analyzed through decomposing the system to a fast subsystem and a slow one. The detailed mechanisms of the wash- out filter on the full dynamical model were given based on the analysis of the fast and the slow subsystem. It was found that the dendritic spike failure was connected to the ＇ ghost＇ of the saddle-node bifurcation of fixed points and the critical point at which the fast subsystem went through a transition from a period-one limit cycle to a period-two limit cycle. Washout filter could change the bifurcation point of local maxima in dendritic potential, and thus change the firing patterns.