This paper deals with a class of inertial quaternion-valued high-order Hopfield neural networks with state-dependent delays. Without decomposing the considered neural networks into real-valued systems, based on a continuation theorem of coincidence degree theory and the Wirtinger inequality, the existence of anti-periodic solutions of the networks is established. By constructing a suitable Lyapunov function, the global exponential stability of anti-periodic solutions of the networks is obtained. Finally, a numerical example is given to show the feasibility of our results.INDEX TERMS Anti-periodic solution, global exponential stability, inertial high-order Hopfield neural networks, quaternion, state-dependent delay.

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In this paper, the existence and stability of Weyl almost automorphic solutions in distribution sense for a class of Clifford-valued stochastic neural networks with time-varying delays are studied by using the direct method. Firstly, the existence and uniqueness of Weyl almost automorphic solutions in distribution sense for this class of neural networks are studied by using the Banach fixed point theorem and the relationship between several different senses of random almost automorphy. Then, the global exponential stability in p th mean of the unique Weyl almost automorphic solution in distribution sense is proved by inequality technique and counter proof method. Even when this class of neural networks we consider is real-valued, our results are new. Meanwhile, the method proposed in this paper can be used to study the existence of Weyl almost automorphic solutions of other types of neural networks including stochastic and deterministic neural networks. Finally, an example is given to illustrate the feasibility of our results.

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