Fin-TS and Fix-TS on fractional quaternion delayed neural networks with uncertainty via establishing a new Caputo derivative inequality approach

• Published in: Mathematical biosciences and engineering : MBE Vol. 19; no. 9; pp. 9220 - 9243
• Main Authors: Wu, Qiong, Yao, Zhimin, Yin, Zhouping, Zhang, Hai
• Format: Journal Article
• Language: English
• Published: AIMS Press 01-01-2022
• Subjects: caputo derivative; distributed delay; fin-ts; fix-ts; fractional differential inequality; quaternion direct method
• ISSN: 1551-0018; 1551-0018
• DOI: 10.3934/mbe.2022428

This paper investigates the finite time synchronization (Fin-TS) and fixed time synchronization (Fix-TS) issues on Caputo quaternion delayed neural networks (QDNNs) with uncertainty. A new Caputo fractional differential inequality is constructed, then Fix-TS settling time of the positive definite function is estimated, which is very convenient to derive Fix-TS condition to Caputo QDNNs. By designing the appropriate self feedback and adaptive controllers, the algebraic discriminant conditions to achieve Fin-TS and Fix-TS on Caputo QDNNs are proposed based on quaternion direct method, Lyapunov stability theory, extended Cauchy Schwartz inequality, Jensen inequality. Finally, the correctness and validity of the presented results under the different orders are verified by two numerical examples.