Intra- and inter-layer dynamics of a two-layer Izhikevich neuron map

In this study, along with a flux controlled memristor for inter-layer synaptic connection, an Izhikevich neuron map of two layer has been built where distance dependent chemical coupling among neurons within each layer. The distance term with power-law factor between neurons placed in a square form is included in the chemical coupling. Dynamic behaviors of intra-layer, inter-layer and total neuron map have been evaluated by changing the coupling strength, distance term and its power law factor. Error term, synchronization factor, and incoherence strength have been used to evaluate simulation results quantitatively. Numerical simulation results show that there are disordered, synchronous and chimera states in both intra- and inter-layers depend on the coupling strength. Furthermore, the memristor layer has also same responses parallel to the intra- and inter-layer. On the other hand, network dynamics have been also effected by distance term and its power law factor. When the distance term is set to unity, as the power-law factor decreases, neuronal nodes achieve to synchronization more quickly for same variation of the chemical coupling strength. However, if coupling strength is set to big enough, the effect of distance term disappears. Moreover, when the power-law factor is adjusted to unity, as the distance term increases, neural network can achieve synchronization with greater chemical coupling strength. Additionally, the simulation results have been verified experimentally on a DSP platform.