Dynamical Analysis of a Tri-Neuron Fractional Network

The present paper concerns with the dynamics of a fractional neural network involving three neurons. Firstly, the bifurcation point is identified for which Hopf bifurcations may occur by taking the system parameter as a bifurcation parameter via the stability analysis of fractional systems. It is indicated that the system parameter can significantly affect the dynamical properties of such network. Secondly, the impact of the order on the bifurcation point is carefully examined. It is found that the occurrence of bifurcation is delayed as the order increases as long as the other system parameters are established. Finally, a numerical example is exploited to verify the efficiency of theoretical results.