  In this paper, the commensurate fractional-order variant of an Hopfield
neuronal network is analyzed. The system is integrated with the ABM method for
fractional-order equations. Beside the standard stability analysis of
equilibria, the divergence of fractional order is proposed to determine the
instability of the equilibria. The bifurcation diagrams versus the fractional
order, and versus one parameter, reveal a strange phenomenon suggesting that
the bifurcation branches generated by initial conditions outside neighborhoods
of unstable equilibria are spurious sets although they look similar with those
generated by initial conditions close to the equilibria. These spurious sets
look ``delayed'' in the considered bifurcation scenario. Once the integration
step-size is reduced, the spurious branches maintain their shapes but tend to
the branches obtained from initial condition within neighborhoods of
equilibria. While the spurious branches move once the integration step size
reduces, the branches generated by the initial conditions near the equilibria
maintain their positions in the considered bifurcation space. This phenomenon
does not depend on the integration-time interval, and repeats in the parameter
bifurcation space.
