Global dissipativity of fuzzy genetic regulatory networks with mixed delays

Abstract

The synthetic genetic regulatory networks have proven to be a powerful tool in studying gene regulation processes in living organisms. In this article, the global dissipativity and corresponding attractive set for the fuzzy genetic regulatory networks with mixed delays are investigated. By utilising the Lyapunov functional method and the linear matrix inequalities (LMIs) techniques, new sufficient conditions ensuring the global dissipativity and the global exponential dissipativity of the suggested system are given. Moreover, the global attractive set and global exponential attractive set are obtained. The derived criteria are of the form of LMI, and hence they can be verified easily by the numerical software. Lastly, two numerical examples with its simulations are given to illustrate the effectiveness of the obtained results.

Keywords:

• Fuzzy genetic regulatory networks
• global dissipativity
• global exponential dissipativity
• mixed delays

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Chaouki Aouiti

Chaouki Aouiti graduated from the Faculty of Sciences of Tunis, University Tunis El Manar (1995). He obtained the M.S. degree in Applied Mathematics from the National Engineering School of Tunis, University Tunis El Manar in 1997.He obtained a PhD and then an HDR both in Applied Mathematics in 2003 and 2017, respectively. He is currently an Associate Professor in Applied Mathematics at Faculty of Sciences of Bizerta, University of Carthage. His research interests include Neural networks, Dynamical systems, Differential equations, Almost periodic differential equation, Almost automorphic differential equation. Dr. Chaouki, currently, serves as a reviewer of several international journals and a Program Committee for various international conferences.

Qing Hui

Qing Hui was previously an associate professor of mechanical engineering at Texas Tech University. His research interests include network robustness and vulnerability analysis, synchronisation and control of network systems, threat detection, biomedical systems, hybrid systems and high-performance scientific computing. Dr. Hui earned Ph.D. in aerospace engineering and a master's of applied mathematics from Georgia Institute of Technology, a master's of automotive engineering from Tsinghua University in China and a bachelor's of aerospace engineering from National University of Defense Technology in China.

Emmanuel Moulay

Emmanuel Moulay received his M.S. degree in mathematics from the University of Lille, France, in 2002. He obtained his Ph.D. degree in automatic control in 2005 from the Ecole Centrale de Lille. He joined the CNRS as a research scientist at the Ecole Centrale de Nantes in 2006 and moved at the XLIM institute of the University of Poitiers in 2009. He is also adjunct professor at the University of Nebraska-Lincoln since 2020. His main interests are in control theory and its practical applications.

Farid Touati

Farid Touati was born in Bizerta, Tunisia. He obtained a Ph.D. in Mathematics at the university of Carthage, Tunisia in 2021. He received her Master's degree in Mathematics from the faculty of Sciences of Bizerta in 2016. His current research field is neutral networks. He is interested in stability, dissipativity and passivity of solutions