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A perspective on graph theory-based stability analysis of impulsive stochastic recurrent neural networks with time-varying delays

Authors
  • Iswarya, M.1
  • Raja, R.1
  • Rajchakit, G.2
  • Cao, J.3
  • Alzabut, J.4
  • Huang, C.5
  • 1 Alagappa University, Karaikudi, India , Karaikudi (India)
  • 2 Maejo University, Chiang Mai, Thailand , Chiang Mai (Thailand)
  • 3 Southeast University, Nanjing, China , Nanjing (China)
  • 4 Prince Sultan University, Riyadh, Saudi Arabia , Riyadh (Saudi Arabia)
  • 5 Changsha University of Science and Technology, Changsha, China , Changsha (China)
Type
Published Article
Journal
Advances in Difference Equations
Publisher
Springer International Publishing
Publication Date
Dec 10, 2019
Volume
2019
Issue
1
Identifiers
DOI: 10.1186/s13662-019-2443-3
Source
Springer Nature
Keywords
License
Green

Abstract

In this work, the exponential stability problem of impulsive recurrent neural networks is investigated; discrete time delay, continuously distributed delay and stochastic noise are simultaneously taken into consideration. In order to guarantee the exponential stability of our considered recurrent neural networks, two distinct types of sufficient conditions are derived on the basis of the Lyapunov functional and coefficient of our given system and also to construct a Lyapunov function for a large scale system a novel graph-theoretic approach is considered, which is derived by utilizing the Lyapunov functional as well as graph theory. In this approach a global Lyapunov functional is constructed which is more related to the topological structure of the given system. We present a numerical example and simulation figures to show the effectiveness of our proposed work.

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