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