Hopf bifurcation of fractional-order small-world networks with time delay

The applicability of small-world networks, which has been significantly extended, is considered in this paper. To obtain more practical solutions, a fractional-order model applied to small-world networks has been firstly tested. The results provide that the time delay assumed as bifurcation parameter can noticeably influence on the dynamics of small-world networks. Moreover, the effects of the fractional order on the stability and bifurcation of the model are performed. In the end, we use the numerical simulation to support the correctness of our theoretical results.