Anti-periodic solutions for quaternion-valued inertial neural networks with time-varying delays
Yongkun Li, Chun Wang · Journal of Intelligent & Fuzzy Systems · 2019
In this paper, we consider a class of quaternion-valued inertial neural networks with time-varying delays. First, by applying a continuation theorem of coincidence degree theory, we establish the existence of anti-periodic solutions of the considered neural networks. Second, by choosing a proper variable substitution, we transform the neural networks into a system of first order differential equations, and by constructing a suitable Lyapunov function, we derive a set of sufficient conditions ensuring the global exponential stability of the system. Finally, we give two examples to illustrate the effectiveness of our results.