Bifurcation analysis in a delayed fractional neural network involving self-connection

The aim of this paper is to analyze the bifurcation for a fractional neural network with self-connection delay involving three neurons. First, by employing the characteristic equation, the bifurcation points of the proposed network are exactly calculated using time delay or the system parameter as a bifurcation parameter, respectively. Second, it is detected that fractional order is conducive to the bifurcation point for such network, and the onset of bifurcation can be markedly deferred or advanced. Third, the bifurcation diagrams are leerily plotted. Finally, to confirm the efficacy of the analytical results, some numerical simulations are rendered.