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In this paper, we are concerned with Clifford-valued cellular neural networks (CNNs) with discrete delays. Since Clifford algebra is a unital associative algebra and its multiplication is noncommutative, to overcome the difficulty of the noncommutativity of the multiplication of Clifford numbers, we first decompose the considered Clifford-valued neural network into 2m2n real-valued systems. Second, based on the Banach fixed point theorem, we establish the existence and uniqueness of almost periodic solutions of the considered neural networks. Then, by designing a novel state-feedback controller and constructing a proper Lyapunov function, we study the global asymptotic synchronization of the considered neural networks. Finally, a numerical example is presented to show the effectiveness and feasibility of our results.

In this paper, we consider a class of Clifford-valued recurrent neural networks (RNNs) with discrete and infinitely distributed delays. In order to overcome the non-commutativity of the multiplication of Clifford numbers, we first transform the Clifford-valued RNNs with discrete and infinitely distributed delays into real-valued systems based on the multiplication rule and properties of Clifford numbers. Then, we establish the existence and uniqueness of almost automorphic solutions for the neural networks under consideration by applying the contraction mapping principle, and we obtain the globally asymptotic almost automorphic synchronization of the neural networks under consideration by designing a novel state feedback controller and constructing an appropriate Lyapunov function. Finally, we present a numerical example to illustrate the feasibility of the results of this paper. INDEX TERMS Clifford-valued recurrent neural networks, time delay, almost automorphic solution, globally asymptotic synchronization.

In this paper, we consider the existence and global exponential stability of pseudo almost automorphic solutions to quaternion-valued cellular neural networks with infinitely distributed delays. Unlike most previous studies of quaternion-valued cellular neural networks, we do not decompose the systems under consideration into real-valued or complex-valued systems, but rather directly study quaternion-valued systems. Our method and the results of this paper are new. An example is given to show the feasibility of our main results.

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In this paper, a class of Clifford-valued stochastic neural network with delays is investigated, by using a direct method, that is, without decomposing the Clifford-valued system into a real-valued system. Based on the contraction mapping principle and contradiction, sufficient conditions are derived to ensure the existence and stability of almost automorphic solutions for the stochastic networks under consideration. Finally, two numerical examples are provided to show the feasibility of our results.

This paper deals with the existence and global exponential stability of almost periodic solutions for quaternion‐valued high‐order Hopfield neural networks with delays by a direct approach. Based on the contraction mapping principle, sufficient conditions are derived to ensure the existence and uniqueness of almost periodic solutions for the networks under consideration. By constructing a suitable Lyapunov function, the global exponential stability criterion of the almost periodic solution are derived. Finally, two numerical examples are given to illustrate the main results of this paper.