Memristor-based model of neuronal excitability and synaptic potentiation

In this manuscript, we investigate the memristor-based implementation of neuronal ion channels in a mathematical model and an experimental circuit for a neuronal oscillator. We used a FitzHugh-Nagumo equation system describing neuronal excitability. Non-linearities introduced by the voltage-gated ion channels were modeled using memristive devices. We implemented three basic neuronal excitability modes including the excitable mode corresponding to a single spike generation, self-oscillation stable limit cycle mode with periodic spike trains and bistability between a fixed point and a limit cycle. We also found the spike-burst activity of mathematical and experimental models under certain system parameters. Modeling synaptic transmission, we simulated postsynaptic response triggered by periodic pulse stimulation. We found that due to the charge accumulation effect in the memristive device, the electronic synapse implemented a qualitatively bio-plausible synapse with a potentiation effect with increasing amplitude of the response triggered by a spike sequence.