Turing instability mechanism of short-memory formation in multilayer FitzHugh-Nagumo network

The study of brain function has been favored by scientists, but the mechanism of short-term memory formation has yet to be precise.

Since the formation of short-term memories depends on neuronal activity, we try to explain the mechanism from the neuron level in this paper.

Due to the modular structures of the brain, we analyze the pattern properties of the FitzHugh-Nagumo model (FHN) on a multilayer network (coupled by a random network). The conditions of short-term memory formation in the multilayer FHN model are obtained. Then the time delay is introduced to more closely match patterns of brain activity. The properties of periodic solutions are obtained by the central manifold theorem.

When the diffusion coeffcient, noise intensity np, and network connection probability p reach a specific range, the brain forms a relatively vague memory. It is found that network and time delay can induce complex cluster dynamics. And the synchrony increases with the increase of p. That is, short-term memory becomes clearer.