Nonlinear dynamics and limit cycle bifurcation of a fractional-order three-node recurrent neural network

In this paper, we introduce the fractional order into a three-node recurrent neural network model, and then consider the effect of the order on the system dynamics for the neural network based on a fractional-order differential equation. By applying the existing theorems on the stability of commensurate fractional-order systems, we investigate the linear stability and Hopf-type bifurcation for the fractional-order neural network model. Our analysis shows that the equilibrium point, which is unstable in the classic integer-order model, can become asymptotically stable in our fractional-order model, which is also confirmed by numerical simulations. Moreover, we also present simulation results of limit cycles produced by the fractional-order neural network model. It is shown that the amplitude of limit cycles increases with the order, while the frequency of limit cycles has robustness against the change in the order due to its small variation.