Stepanov-Like Pseudo Almost Periodic Solution of Quaternion-Valued for Fuzzy Recurrent Neural Networks with Mixed Delays

Real-valued neural networks or complex-valued neural networks are sometimes inappropriate for some engineering and research problems for instance where the data is multi-dimensional, such as 4-D signals, color images and body images. Hence, researchers explored recently a more general and sophisticated model than the previous one, which is the quaternion-valued neural networks. The quaternions, which can also be defined as 2× 2 matrix of complex numbers, have the capacity to analyze three or more dimensional signals and represent spatial transformations. In this paper, some sufficient conditions are given for the existence and various kinds of stability for the unique Stepanov-like pseudo almost periodic solution of quaternion-valued fuzzy recurrent neural networks. The results are established by employing Lyapunov functionals, Nemytskii’s operator and Banach fixed point theorem. Also, a new direct method is used to establish our theoretical results in order to avoid the decomposition of the considered model into real-valued or complex-valued system. Finally, a numerical example is given to illustrate the validity of the obtained results.