Emitting waves from defects in network with autapses

Autapse is an unusual type of synapse generated by a neuron on itself. The effect of autapse connected to a neuron is often described by using a self-feedback forcing current in a close loop, and the electric activities of neuron can be regulated by the autapse greatly. Generally, positive feedback in the autapse can excite the quiescent neuron while negative feedback often calms down the excitable neuron. In this paper, the Hindmarsh–Rose neuron model is used to define the local kinetics of each node in the neuronal network, and the distribution of autapses in the network is considered to investigate the emergence of emitting wave induced by autapse (in electrical type) with negative feedback. In the case of ring network, it is found that pulse can be blocked by the neurons with negative feedback in autapse, and the pulse also can keep alive in the ring network stably under appropriate coupling intensity. Furthermore, target wave can be induced in the two-dimensional square array, and the nodes adjusted by negative electrical feedback type in autapses can emit target-like waves to regulate the collective behaviors of neurons, this is a new type of wave formation results from diffraction. It concludes that local distribution of autapse with negative feedback type can generate ‘defects’ in the network, the diversity in excitability accounts for the emergence of emitting wave from these defects. Finally, the functional switch between negative and positive feedback in autapse is discussed, it is claimed that positive feedback autapse plays an important role in cheering up quiescent neurons, while the negative feedback in electric autapse can contribute to slow down the excitable neurons.