Exponential synchronisation of linearly coupled reaction-diffusion neural networks with discrete and infinite distributed delays

ABSTRACT

This paper presents the exponential synchronisation for linearly coupled reaction-diffusion neural networks (CRDNNs) with discrete, infinite distributed delays and Dirichlet boundary condition. Two sufficient criteria are obtained for the exponential synchronisation of linearly coupled semi-linear diffusion partial differential equations (PDEs) with discrete, infinite distributed time-delays by using the Halanay inequality and Lyapunov-Krasoviskii functional stability scheme. These results are presented by linear matrix inequality and solved by MATLAB LMI Toolbox. Two simulation examples of linearly CRDNNs with discrete, infinite distributed delays are given to illustrate the validity of the results obtained above.

KEYWORDS:

• Coupled reaction-diffusion neural networks
• exponential synchronisation
• partial differential system
• linear matrix inequality
• infinite distributed delay

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Ping He http://orcid.org/0000-0001-7340-9606

Heng Li http://orcid.org/0000-0002-3187-9041

Xiaochun Luo http://orcid.org/0000-0002-2497-848X

Mali Xing http://orcid.org/0000-0002-4583-8590

Additional information

Funding

This work was jointly supported by the National Natural Science Foundation of China (grants 11705122, 61803098, and 61902268), Outstanding Youth Backbone Project of Jinan University (grant 2019QNGG26), Hong Kong Research Grants Council (grants BRE/PolyU 152099/18E, and PolyU 15204719/18E), Natural Science Foundation of The Hong Kong Polytechnic University (grant G-YW3X), Sichuan Science and Technology Program (grants 20GJHZ0138, 2019YFSY0045, 2018GZDZX0046, and 2018JY0197), Guangxi Natural Science Foundation of China (grant 2018GXNSFAA138092), Open Foundation of Artificial Intelligence Key Laboratory of Sichuan Province (grant 2018RZJ01), Nature Science Foundation of Sichuan University of Science and Engineering (grant 2017RCL52), Zigong Science and Technology Program of China (grants 2019YYJC03, 2019YYJC15).

Notes on contributors

Ping He

Ping He received Ph.D. degree in Electromechanical Engineering from Universidade de Macau, Macao. Since December 2018, he has been a Full Professor with Jinan University, Zhuhai, Guangdong, China. He is the author of one book, and more than 50 articles. His research interests include robot, sensor networks, complex networks, multi-agent systems, artificial intelligence, and control engineering. He is the Reviewer Member for Mathematical Reviews of American Mathematical Society (Reviewer Number: 139695). He also serves as a Section Editor of Automatika: Journal for Control, Measurement, Electronics, Computing and Communications, an Academic Editor of PLOS ONE, and an Associate Editor of Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering and IET The Journal of Engineering. Dr. Ping He is the corresponding author and can be contacted at E-mail address: [email protected]; [email protected]

Heng Li

Heng Li was born in Hunan Province, PR China, in 1963. He received the B.S. and M.S. degrees in Civil Engineering from Tongji University, in 1984 and 1987 respectively; and the Ph.D. degree in Architectural Science from the University of Sydney, Australia in 1993. Form 1993–1995, he was a Lecturer at James Cook University. During 1996-1997, he was a Senior Lecture in the Civil Engineering Department at Monash University. Since 1997, he was gradually promoted from Associate Professor to his current position: Chair professor of Construction Informatics at The Hong Kong Polytechnic University. He is the author of 2 books and more than 500 articles. His research interests include building information modelling, robotics, functional materials; and internet of things. Dr. Li was a recipient of National award from Chinese Ministry of Education in 2015; and Gold Prize of Geneva Innovation 2019. He is also a Reviews Editor of Automation in Construction.

Xiaochun Luo

Xiaochun Luo received the PhD degree in construction informatics from the Hong Kong Polytechnic University in 2010. He is now a senior research fellow of the Smart Construction Lab, the Hong Kong Polytechnic University. His current research focuses on statistical machine learning, studying and predicting how computer vision, wireless sensors, and digital construction are changing product quality, productivity, occupational safety and health in construction.

Mali Xing

Mali Xing was born in 1990. She received her Ph.D. degree in systems engineering from South China University of Technology, Guangzhou, in October 2017. Since December 2017, she has been a lecturer with Guangdong University of Technology. Her current research interests include multi-agent systems and stochastic systems. Dr. Mali Xing has published more than thirty scientific papers in professional international peer-reviewed journals.