Dynamics of fractional-order neural networks

In this paper we discuss the stability analysis for fractional-order neural networks of Hopfield type. The stability domain of a steady state is completely characterized with respect to some characteristic parameters of the system, in the case of a two-dimensional network and of a network of n ≥ 3 neurons with ring structure. The values of the characteristic parameters for which Hopf bifurcations occur are identified. Numerical simulations are given which substantiate the theoretical findings and suggest possible routes towards chaos when the fractional order of the system increases.