Attractor in circular structure of oscillatory generalized neural elements

A perspective model of a neuron cell — the generalized neural element (GNE) is studied in this article. The model has an universal character. It combines properties of a neuron-oscillator and a neuron-detector. In this structure cyclic sequential pulse generation elements of the ring are studied. A nonlinear mapping for mismatches between pulses of neighboring elements is constructed. We prove the existence of a fixed point of this mapping (threshold value of mismatches) and its stability in a small neighborhood of the fixed point. In doing so the existence of a stable oscillatory mode of neural activity (attractor) of a certain type is proved. The parameters of the attractor (threshold values of mismatches) can be controlled in advance, due to the choice of synaptic weights of the links in the ring.