Autapse-induced target wave, spiral wave in regular network of neurons

Autapse is a type of synapse that connects axon and dendrites of the same neuron, and the effect is often detected by close-loop feedback in axonal action potentials to the owned dendritic tree. An artificial autapse was introduced into the Hindmarsh-Rose neuron model, and a regular network was designed to detect the regular pattern formation induced by autapse. It was found that target wave emerged in the network even when only a single autapse was considered. By increasing the (autapse density) number of neurons with autapse, for example, a regular area (2x2, 3x3, 4x4, 5x5 neurons) under autapse induced target wave by selecting the feedback gain and time-delay in autapse. Spiral waves were also observed under optimized feedback gain and time delay in autapses because of coherence-like resonance in the network induced by some electric autapses connected to some neurons. This confirmed that the electric autapse has a critical role in exciting and regulating the collective behaviors of neurons by generating stable regular waves (target waves, spiral waves) in the network. The wave length of the induced travelling wave (target wave, spiral wave), because of local effect of autapse, was also calculated to understand the waveprofile in the network of neurons.