Complex regimes in electronic neuron-like oscillators with sigmoid coupling

Abstract

The new version of electronic implementation of FitzHugh–Nagumo neuron model was proposed together with a new circuit for synapse (sigmoid activation function). The proposed neuron and synapse models provide better representation of activation function in biological neurons including possibility to model excitatory and inhibitory connections. Various regimes in two FitzHugh–Nagumo neurons were studied numerically and in hardware experiment. Different scenarios of oscillation emergence were investigated, including saddle-node cycle bifurcation leading to appearance of highly nonlinear limit cycles of large amplitude. Long living transients near these bifurcations were found those are of particular interest for modeling some metastable phenomena in living systems like sleep and epilepsy.