Finite-/fixed-time synchronization of delayed Clifford-valued recurrent neural networks

• Published in: Advances in difference equations Vol. 2021; no. 1; pp. 1 - 25
• Main Authors: Boonsatit, N., Rajchakit, G., Sriraman, R., Lim, C. P., Agarwal, P.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 03.06.2021; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Clifford-valued neural network; Difference and Functional Equations; Feedback control; Finite-time; Fixed-time; Functional Analysis; Lyapunov–Krasovskii functional; Mathematics; Mathematics and Statistics; Multiplication; Neural networks; Ordinary Differential Equations; Partial Differential Equations; Recurrent neural networks; Synchronization; Time synchronization; Clifford-valued neural network; Finite-time; Fixed-time; Synchronization; Lyapunov–Krasovskii functional
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-021-03438-1

This paper investigates the problem of finite-/fixed-time synchronization for Clifford-valued recurrent neural networks with time-varying delays. The considered Clifford-valued drive and response system models are firstly decomposed into real-valued drive and response system models in order to overcome the difficulty of the noncommutativity of the multiplication of Clifford numbers. Then, suitable time-delayed feedback controllers are devised to investigate the synchronization problem in finite-/fixed-time of error system. On the basis of new Lyapunov–Krasovskii functional and new computational techniques, finite-/fixed-time synchronization criteria are formulated for the corresponding real-valued drive and response system models. Two numerical examples demonstrate the effectiveness of the theoretical results.