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

• Main Authors: M. Iswarya, R. Raja, G. Rajchakit, J. Cao, J. Alzabut, C. Huang
• Format: Article
• Language: English
• Published: SpringerOpen 2019-12-01
• Series: Advances in Difference Equations
• Subjects: Recurrent neural networks (RNNs); Exponential stability; Graph theory; Young’s inequality; Discrete time-varying delays; Infinite distributed time-varying delays
• Online Access: https://doi.org/10.1186/s13662-019-2443-3

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.