Almost automorphic dynamics to stochastic octonion-valued fuzzy neural networks with delays

In this paper, we are concerned with the almost automorphic dynamics for a class of stochastic octonion-valued fuzzy neural networks (SOVFNNs) with delays. Using a non-decomposition approach and without assuming that the activation functions satisfy the global Lipschitz condition, we investigate the existence and uniqueness of almost automorphic solutions in finite-dimensional distributions to this class of SOVFNNs and the global exponential stability of the unique almost automorphic solution in mean square sense, respectively. Firstly, we use the Banach contraction principle to establish the existence of a unique $L^2$-bounded and $L^2$-uniformly continuous solution of SOVFNNs in a suitable complete space. Then, we employ some inequality tricks to demonstrate that this unique solution is also an almost automorphic one in finite-dimensional distributions. In addition, we establish the global exponential stability of this almost automorphic solution by contradiction method. Finally, we present an example to validate the obtained results. The results gained in this paper are completely new even when the SOVFNNs degenerate into real-valued neural networks (RVNNs).