Hopf bifurcation in a fractional-order neural network with self-connection delay

This paper is concerned with the bifurcation problem of a two-delayed fractional-order neural network(FONN) with three neurons. To begin with, the bifurcation progresses with regard to some types of time delays are captured by employing the self-connecting delay as a bifurcation parameter. Afterwards, communication delay is viewed as a bifurcation parameter to cultivate bifurcation outcomes for the developed FONN, and the communication delay triggered-bifurcation conditions are captured. There is an evidence that FONN emanates remarkable stability as long as a smaller value of them is selected, and the stability performance deterioration and Hopf bifurcations take place once choosing a larger control time delay. Eventually, the correctness of the developed theoretical discoveries is appraised by employing numerical revelations.