Existence and Global Stability of Periodic Solution for Delayed Discrete High-order Hopfield-type Neural Networks

It is well known that studies on neural dynamical systems not only involve discussion of stability property, but also involve other dynamics behaviors such as periodic oscillatory, bifurcation and chaos. In many applications, the property of periodic oscillatory solutions are of great interest. For example, the human brain has been in periodic oscillatory or chaos state, hence it is of prime importance to study periodic oscillatory and chaos phenomenon of neural networks. Recently, Liu and Liao [8], Zhou and Liu [15] consider the existence and global exponential stability of periodic solutions of delayed Hopfield neural networks and delayed cellular neural networks. Liu et al. [7] address the existence and global exponential stability of periodic solutions of delayed BAM neural networks. Since high-order neural networks have stronger approximation property, faster convergence rate, greater storage capacity, and higher fault tolerance than lower-order neural networks, they have attracted considerable attention (see, e.g., [1, 2, 4, 5, 10, 11, 13, 14]). In our previous paper [12], we study the global exponential stability and existence of periodic solutions of the following high-order Hopfield-type neural networks