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Octonion-valued neural networks (OVNNs) are a type of neural networks forwhich the states and weights are octonions. In this paper, the global$\mu$-stability and finite-time stability problems for octonion-valued neuralnetworks are considered under unbounded and asynchronous time-varying delays.To avoid the non-communicative and non-associative multiplication feature ofthe octonions, we firstly decompose the OVNNs into eight real-valued neuralnetworks (RVNNs) equivalently. Through the use of generalized norm and theCauchy convergence principle, we obtain the sufficient criteria which assurethe existence, uniqueness of the equilibrium point and global $\mu$-stabilityof OVNNs. By adding controllers, the criteria to ensure the finite-timestability for OVNNs are presented by dividing the analysis of finite-timestability process into two phases. Furthermore, we also prove the adaptivefinite time stability theory of above networks. At last, the simulation resultsof specified examples is given to substantiate the effectiveness andcorrectness of the theoretical results.

Global $\mu$-stability and finite-time control of octonion-valued neural networks with unbounded delays