Existence and exponential stability of solutions for quaternion-valued delayed hopfield neural networks by ξ-Norms
- Institute of Electrical and Electronics Engineers (IEEE)
- Publication Type:
- Journal Article
- IEEE Access, 2019, 7, pp. 184509-184517
- Issue Date:
© 2013 IEEE. Recently, with the development of quaternion applications, quaternion-valued neural networks (QVNNs) have been presented and studied by more and more scholars. In this paper, the existence, uniqueness and exponential stability criteria of solutions for the quaternion-valued delayed Hopfield neural networks (QVDHNNs) are mainly investigated by means of the definitions of ξ-norms. In order to construct a ξ-norm, QVDHNNs system are decomposed into four real-number systems according to Hamilton rules. Then, taking advantage of ξ-norms, inequality technique and Cauchy's test for convergence, time-invariant delays and time-varying delays are considered successively to derive ξ-exponential type sufficient conditions. Based on these, several corollaries about the existence, uniqueness and exponential stability of solutions are obtained. Finally, two numerical examples with time-invariant delays and time-varying delays are given respectively. Their simulated images illustrate the effectiveness of the main theoretical results.
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