Effects of the short-cut connection on the dynamics of a delayed ring neural network

This paper studies quantitatively a high dimensional delayed neural network with small world connection. On the basis of Lyapunov stability approach, we investigate the asymptotic stability of the trivial equilibrium and obtain delay-dependent criteria ensuring global stability for the neural network. It shows that the small world connection decreases the global stability interval. Special attention is paid to the complex dynamics due to the short-cut connenction. Some complex dynamical behaviors are exhibited numerically such as period-doubling bifurcation and quasi-period bifurcation to chaos. It would be promising that small world connection can be used as an effective scheme to control the dynamics.