A phenomenological model of a pair of neurons is considered, where each neuron is described by a relay delay differential equation. The first equation is a relay-based simplification of the generalized Hutchinson equation. The only stable behavior exhibited by this neuron is the spiking mode. The second neuron is also modeled using a relay simplification of the generalized Hutchinson equation, with an additional coupling term linking it to the first neuron. This study demonstrates that the equation governing the second neuron exhibits significantly richer dynamics compared to the first. In particular, fading and reviving neuron regimes, as well as a chaotic regime, have been identified.