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Nonlinear Dynamics

, Volume 79, Issue 2, pp 1085–1098 | Cite as

Exponential input-to-state stability of stochastic Cohen–Grossberg neural networks with mixed delays

  • Quanxin Zhu
  • Jinde Cao
  • R. Rakkiyappan
Original Paper

Abstract

In this paper, we study an issue of input-to-state stability analysis for a class of impulsive stochastic Cohen–Grossberg neural networks with mixed delays. The mixed delays consist of varying delays and continuously distributed delays. To the best of our knowledge, the input-to-state stability problem for this class of stochastic system has still not been solved, despite its practical importance. The main aim of this paper is to fill the gap. By constricting several novel Lyapunov–Krasovskii functionals and using some techniques such as the It\(\hat{o}\) formula, Dynkin formula, impulse theory, stochastic analysis theory, and the mathematical induction, we obtain some new sufficient conditions to ensure that the considered system with/without impulse control is mean-square exponentially input-to-state stable. Moreover, the obtained results are illustrated well with two numerical examples and their simulations.

Keywords

Exponential input-to-state stability Stochastic Cohen–Grossberg neural network  Varying delay Continuously distributed delay  Impulse control 

Notes

Acknowledgments

The work of the first author was jointly supported by the National Natural Science Foundation of China (61374080), the Natural Science Foundation of Zhejiang Province (LY12F 03010), the Natural Science Foundation of Ningbo (2012A61 0032), and a Project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions; Jinde Cao’s work was jointly supported by the National Natural Science Foundation of China (61272530, 11072059), and the Specialized Research Fund for the Doctoral Program of Higher Education (20110092110017); R. Rakkiyappan’s work was supported by NBHM Research Project.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of Mathematical Sciences, Institute of Finance and StatisticsNanjing Normal UniversityNanjingChina
  2. 2.Department of MathematicsSoutheast UniversityNanjingChina
  3. 3.Department of MathematicsBharathiar UniversityCoimbatoreIndia

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