Novel Lagrange sense exponential stability criteria for time-delayed stochastic Cohen–Grossberg neural networks with Markovian jump parameters: A graph-theoretic approach
Articles
Iswarya Manickam
Alagappa University
Raja Ramachandran
Alagappa University
Grienggrai Rajchakit
Maejo University
Jinde Cao
Southeast University
Chuangxia Huang
Changsha University of Science and Technology
Published 2020-09-01
https://doi.org/10.15388/namc.2020.25.16775
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Keywords

Cohen–Grossberg neural networks
Lagrange stability
graph theory
discrete and distributed time delays

How to Cite

Manickam I., Ramachandran R., Rajchakit G., Cao J. and Huang C. (2020) “Novel Lagrange sense exponential stability criteria for time-delayed stochastic Cohen–Grossberg neural networks with Markovian jump parameters: A graph-theoretic approach”, Nonlinear Analysis: Modelling and Control, 25(5), pp. 726–744. doi: 10.15388/namc.2020.25.16775.

Abstract

This paper concerns the issues of exponential stability in Lagrange sense for a class of stochastic Cohen–Grossberg neural networks (SCGNNs) with Markovian jump and mixed time delay effects. A systematic approach of constructing a global Lyapunov function for SCGNNs with mixed time delays and Markovian jumping is provided by applying the association of Lyapunov method and graph theory results. Moreover, by using some inequality techniques in Lyapunov-type and coefficient-type theorems we attain two kinds of sufficient conditions to ensure the global exponential stability (GES) through Lagrange sense for the addressed SCGNNs. Ultimately, some examples with numerical simulations are given to demonstrate the effectiveness of the acquired result.

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