Spiral wave in a two-layer neuronal network

Multi-layer networks are quite fundamental to study structural and functional properties of various biological systems. In this study, a two-layer neuronal network is considered and the interactions between the spiral pattern in one layer and a homogeneous state in the other layer, under the effect of inter-layer bidirectional connection are investigated. Spiral wave has been confirmed to play a significant role in many complex systems. In this regard, in laminar structured systems in particular, it is crucial to study the dynamics of the spiral wave affected by the inter-layer interactions. Here, for each layer (sub-network), a regular network with eight-neighbor connection is designed. For the local dynamics of each neuron, the magnetic Fitzhugh-Nagumo (FN) neuronal model is introduced. The results show that depending on the level of interactions between the two layers, four different types of collective electrical activity can occur. When the inter-layer connection is weak, the layer with spiral pattern does not change while the homogeneous state of the other layer is broken by a blurred spiral pattern. As the inter-layer connection is strengthened, the dynamics of the spiral wave changes significantly, leading to unstable spiral wave and spiral turbulence. However, by a further increase in the inter-layer coupling strength, the spiral wave does not exist at all.