Delayed afterdepolarization and spontaneous secondary spiking in a simple model of neural activity

In this paper we suggest a new dynamical model of neuron excitability. It is based on the classical FitzHugh–Nagumo model in which we introduce the third variable for additional ionic current. By using the method of fast and slow motions we study the afterdepolarization, spontaneous secondary spiking and tonic spiking effects. We build regions in the parameter space that correspond to different dynamical regimes. The obtained results may be important for different problems of neuroscience, e.g. for the problem of working memory.

► A dynamical mechanism of delayed afterdepolarization and secondary spiking is explained.
► Spontaneous spiking appears through the saddle-node bifurcation of periodic motions.
► Transition between the ADP and spontaneous spiking occurs through producing of finite number of secondary spikes.