Mean-square exponential input-to-state stability for stochastic neutral-type quaternion-valued neural networks via Itô’s formula of quaternion version

The input-to-state stability of stochastic quaternion-valued neural networks with neutral delays is explored in this study. Unlike previous researches, this study treats the neural network as a unified entity, rather than isolating and examining the real and imaginary components separately. Through the construction of a Lyapunov functional and the use of the Itô’s formula of quaternion version, a sufficient criterion for achieving mean-square exponential input-to-state stability is obtained for stochastic quaternion-valued neural networks with neutral delays. Three numerical instances are presented to validate the reliability of the obtained conditions.