Dynamics of electric activities in neuron and neurons of network induced by autapses

The effect of autapse on adjusting the membrane of potentials of neuron is described by imposing a time-delayed feedback on the membrane of neuron in a close loop type, and the Hindmarsh-Rose (HR) neuron under autapse is investigated. Firstly, the electric activity of single HR neuron under electric autapse and chemical autapse is investigated. It is found that quiescent neuron is activated due to appropriate time delay and feedback gain in the autapse, and the autapse plays an important role in waking up neuron. The parameter region for periodic, chaotic activity of neuron under autapse is calculated in a numerical way, and transition from spiking to bursting is observed by increasing the feedback gain and time delay carefully. Furthermore, the collective electric activities of neurons in a ring network is investigated and abundant electric activities are observed due to the competition between the autapse and the time-delayed coupling between adjacent neurons in the network, and time delay in coupling between neurons also plays an important role in enhancing synchronization in the network.