This paper proposes a class of quaternion-valued high-order Hopfield neural networks with delays. By using the non-decomposition method, non-reduced order method, analytical techniques in uniform convergence functions sequence, and constructing Lyapunov function, we obtain several sufficient conditions for the existence and global exponential synchronization of anti-periodic solutions for delayed quaternion-valued high-order Hopfield neural networks. Finally, an example and its numerical simulations are given to support the proposed approach. Our results play an important role in designing inertial neural networks.

In this paper, we propose a class of octonion-valued neural networks with leakage delays and mixed delays. Considering that the multiplication of octonion algebras does not satisfy the associativity and commutativity, we can obtain the existence and global exponential stability of weighted pseudo almost periodic solutions for octonion-valued neural networks with leakage delays and mixed delays by using the Banach fixed point theorem, the proof by contradiction and the non-decomposition method. Finally, we will give one example to illustrate the feasibility and effectiveness of the main results.