Global exponential convergence of neutral-type competitive neural networks with multi-proportional delays, distributed delays and time-varying delay in leakage delays

Abstract

This paper is concerned with a class of neutral-type competitive neural networks with multi-proportional delays, distributed delays and leakage delays. By employing the differential inequality theory, some sufficient conditions are given to ensure that all solutions of the addressed system converge exponentially to zero vector. An illustrative example is also given at the end of this paper to show the effectiveness of our results.

Keywords:

• Neutral-type competitive neural networks
• leakage delay
• proportional delay
• exponential convergence

Acknowledgments

The authors would like to express their sincere thanks to the referees for suggesting some corrections that help making the content of the paper more accurate.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ahmed Alsaedi http://orcid.org/0000-0003-3133-7119

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.

El abed Assali

El abed Assali was born in Foussana, Tunisia. He received a Master of research in Mathematics from the Faculty of Sciences of Bizerta (FSB) at the University of Carthage (Tunisia) in 2016. Currently, he is working towards the Ph.D. degree in Mathematics at University of Carthage. His major research interests include stability theory, neural networks, impulsive dynamical systems, pseudo-almost periodic solutions.

Jinde Cao

Jinde Cao (M'07–SM'07–F'16) is a Distinguished Professor, the Dean of School of Mathematics and the Director of the Research Center for Complex Systems and Network Sciences at Southeast University. From March 1989 to May 2000, he was with the Yunnan University. In May 2000, he joined the School of Mathematics, Southeast University, Nanjing, China. From July 2001 to June 2002, he was a Postdoctoral Research Fellow at the Department of Automation and Computer-Aided Engineering, Chinese University of Hong Kong, Hong Kong. Professor Cao was an Associate Editor of the IEEE Transactions on Neural Networks, Journal of the Franklin Institute, Neurocomputing, and Differential Equations and Dynamical Systems. He is currently an Associate Editor of the IEEE Transactions on Cybernetics, IEEE Transactions on Cognitive and Developmental Systems, Neural Networks, Nonlinear Analysis: Modeling and Control, Mathematics and Computers in Simulation, Cognitive Neurodynamics, Advances in Difference Equations, and Journal of Artificial Intelligence and Soft Computing Research. He is a Fellow of IEEE, and a Member of the Academy of Europe. He has been named as Highly-Cited Researcher in Engineering, Computer Science, and Mathematics by Thomson Reuters. He received the National Award for Excellence in Innovation (2017).

Ahmed Alsaedi

Ahmed Alsaedi received his Ph.D. degree from Swansea University (UK) in 2002. He has a broad experience of research in applied mathematics. His fields of interest include dynamical systems, nonlinear analysis involving ordinary differential equations, fractional differential equations, boundary value problems, mathematical modeling, biomathematics, Newtonian and Non-Newtonian fluid mechanics. He has published several articles in peer-reviewed journals. He supervised several M.S/Ph.D students and executed many funded research projects. He is a reviewer of several international journals. He served as the chairman of the mathematics department at KAU and presently he is serving as director of the research program at KAU. Under his great leadership, this program is running quite successfully, and it has attracted a large number of highly rated researchers and distinguished professors from all over the world. He is also the head of NAAM international research group at KAU.