Stepanov-Like Pseudo Almost Automorphic Dynamics of QVRNNS with Mixed Delays on Time Scales via a Direct Method

A BSTRACT . In this paper, we are concerned with a class of quaternion-valued recurrent neutral neural networks (QVRNNs) with time-varying delays and infinite distributed delays on time scales. With the help of the Stepanov like pseudo almost automorphy on time scales, Banach’s fixed point theorem, the theory of time scale calculations, and constructing a suitable Lyapunov functional, a set of sufficient criteria that guarantee the existence, uniqueness and the globally S p -exponential stability of Stepanov-like pseudo almost automorphic solution on time scales of this class of neural networks are established via a direct method. In other words, we do not decompose the considered QVRNNs into real-valued systems or complex-valued systems. Finally, two numerical examples and simulations (for T = R and Z ) are performed to verify our theoretical results.