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

Qiong Wu; Zhimin Yao; Zhouping Yin; Hai Zhang; Qiong Wu; Zhimin Yao; Zhouping Yin; Hai Zhang

doi:10.3934/mbe.2022428

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 9: 9220-9243. doi: 10.3934/mbe.2022428

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

School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China

Academic Editor: Xiaodi Li

Received: 19 May 2022 Revised: 13 June 2022 Accepted: 21 June 2022 Published: 23 June 2022

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.

Keywords:

Citation: Qiong Wu, Zhimin Yao, Zhouping Yin, Hai Zhang. Fin-TS and Fix-TS on fractional quaternion delayed neural networks with uncertainty via establishing a new Caputo derivative inequality approach[J]. Mathematical Biosciences and Engineering, 2022, 19(9): 9220-9243. doi: 10.3934/mbe.2022428

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Abstract

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