Mittag‐Leffler stability and synchronization of discrete‐time quaternion valued delayed neural networks with fractional order and its application

Author:

Zhang Weiwei12ORCID,Wang Guanglan3,Sha Chunlin1,Cao Jinde45

Affiliation:

1. College of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing China

2. School of Mathematics and Physics Anqing Normal University Anqing China

3. College of Continuing Education Nanjing University of Aeronautics and Astronautics Nanjing China

4. School of Mathematics Southeast University Nanjing China

5. Yonsei Frontier Lab Yonsei University Seoul South Korea

Abstract

This paper discusses the problem of Mittag‐Leffler stability and synchronization for discrete‐time fractional‐order delayed quaternion valued neural networks (DTFODQVNN). Firstly, a criterion is achieved to ensure the existence and uniqueness of the equilibrium point (EP) of DTFODQVNN through applying Brouwer's fixed‐point theory. Secondly, based on a Lyapunov function and a new discrete fractional inequality, the stability condition is established by employing a linear matrix inequality approach. In addition, by constructing a proper controller, drive–response synchronization is investigated by means of deploying Lyapunov direct method (LDM). Finally, two examples with simulations test the correctness of the acquired results. Moreover, image encryption is considered as an application based on the chaotic DTFODQVNN.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Anhui Province

Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province

Publisher

Wiley

Reference52 articles.

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3. Quaternion-Valued Echo State Networks

4. Quaternion neural network with geometrical operators;Matsui N.;J. Intell. Fuzzy Syst.,2014

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