Periodic Solution For Quaternion Valued Inertial Neural Networks With Time-Varying Delay

In this paper,we study the existence and global exponential stability of periodic solution for a wide class of quaternion-valued inertial neural networks with time-varying delays.First,by properly chosing variable substitution the system is transformed to the first order differential equation.Secondly,by combining the continuation theorem of Mawhin's coincidence degree theory and by using inequality techniques,a sufficient condition on the existence of periodic solutions for quaternion-valued inertial neural net-works is obtained.By constructing a new Lyapunov functional method,some sufficient condition are derived to ensure the global exponential stability of periodic solutions for quaternion-valued inertial neural networks.Finally,two examples are given to illustrate the effectiveness of the obtained results.