Controlling the firing patterns around a saddle-node bifurcation in the ghostburster model

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 washout 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.