Stability analysis of Clifford-valued memristor-based neural networks with impulsive disturbances and its application to image encryption.

In this paper, a type of delayed Clifford-valued memristor-based neural networks (CLVMNNs) with impulsive disturbances is established, and the global exponential stability is investigated by using generalized norm. Firstly, the n-dimensional Clifford-valued systems are decomposed into 2 m n -dimensional real-valued systems to address the non-commutativity problem of the multiplication of Clifford numbers. Secondly, the generalized ∞-norm and 1-norm are introduced to induce the global exponential stability for CLVMNNs, and two special Lyapunov functionals are established to prove the stability. Thirdly, the strict assumption of the boundedness of activation function in previous research is loosened, and some less conservative conditions of stability are obtained based on the constructed Lyapunov functionals. Finally, the theoretical results are verified by two numerical simulations, and an image encryption scheme is proposed to show the application in real world situation based on the delayed CLVMNNs. • Impulsive disturbances and memristor are taken into account for Clifford-valued NNs. • The generalized { ξ , 1 } -norm and { ξ , ∞ } -norm are introduced to investigate the global exponential stability of CLVMNNs. • The global exponential stability of CLVMNNs is discussed and some new criteria are derived. [ABSTRACT FROM AUTHOR]