Asymptotic behavior of Clifford-valued dynamic systems with D-operator on time scales

Abstract

Abstract In this paper, a general class of Clifford-valued neutral high-order neural network (HNN) with D-operator on time scales is investigated. In this model, time-varying delays and continuously distributed delays are taken into account. As an extension of the real-valued neural network, the Clifford-valued neural network, which includes a familiar complex-valued neural network and a quaternion-valued neural network as special cases, has been an active research field recently. By utilizing this novel method, which incorporates the differential inequality techniques and the fixed point theorem and time-scale theory of computation, we derive a few sufficient conditions to ensure the existence, uniqueness, and exponential stability of the pseudo almost periodic (PAP) solution of the considered model. The results in this paper are new, even if time scale T = R $\mathbb{T}=\mathbb{R}$ or T = Z $\mathbb{T}=\mathbb{Z}$ , and complementary to the previously existing works. Furthermore, an example and its numerical simulations are included to demonstrate the validity and advantage of the obtained results.

Keywords

• Clifford-valued
• Neutral type
• High-order neural networks
• Time scales
• Global exponential stability
• Pseudo almost periodic function