Bifurcation and oscillations in fluidic nanopores: A model neuron for liquid neuromorphic networks

Neuron spiking constitutes the central information node in neural networks. Nanoscale fluidic pores with rectification and hysteresis provide the opportunity to induce voltage oscillations with the same physical principles as in living neurons. We establish the conditions that enable self-sustained limit-cycle oscillations in a single artificial pore channel by a Hopf bifurcation, thus providing the minimal model for the elementary neuron. On a fluidic nanochannel that contains the necessary ingredients as the capacitive and inductive response and a stationary negative resistance, we identify the range of physical parameters where oscillations occur. These results provide crucial guidelines for identifying the conditions to build the oscillating nanopore according to the system's geometrical, electrical, fluidic, and chemical variables, which otherwise could be overlooked, since the relevant parameter region producing oscillations can be narrow.