Weak, modified and function projective synchronization of Cohen–Grossberg neural networks with mixed time-varying delays and parameter mismatch via matrix measure approach
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This paper is concerned with the modified function projective synchronization of Cohen–Grossberg neural networks systems with parameter mismatch and mixed time-varying delays. Due to the existence of parameter mismatch between the drive and slave systems, complete modified function projective synchronization is not possible to achieve. So a new concept, viz., weak modified function projective synchronization, is discussed up to a small error bound. Several generic criteria are derived to show weak modified function projective synchronization between the systems. The estimation of error bound is done using matrix measure and Halanay inequality. Simulation results are proposed graphically for different particular cases to show the synchronization between parameter-mismatched systems, which validate the effectiveness of our proposed theoretical results.
KeywordsNeural networks Mixed time-varying delays Halanay inequality Matrix measure Modified function projective synchronization
The authors are extending their heartfelt thanks to the revered reviewers for their constructive suggestions toward up-gradation of the article.
Compliance with ethical standards
Conflict of interest
The authors Subir Das, Professor, Department of Mathematical Sciences, IIT (BHU), Varanasi, India, and Mr. Rakesh Kumar, who is pursuing his Ph.D. degree under the supervision of Prof. S. Das, declare that they have no conflict of interest.
- 14.Feng Yl, Wang Jc (2010) Modified projective synchronization of the unified chaotic system. J Zhangzhou Norm Univ (Nat Sci) 3:005Google Scholar
- 20.Hongyue D, Qingshuang Z, Mingxiang L (2008) Adaptive modified function projective synchronization with known or unknown parameters. In: IEEE international symposium on knowledge acquisition and modeling workshop, 2008. KAM Workshop 2008Google Scholar
- 25.Li K, Song Q (2008) Exponential stability of impulsive Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms. Neurocomputing 72(1–3):231–240Google Scholar
- 26.Li T, Song AG, Fei SM (2009) Robust stability of stochastic Cohen–Grossberg neural networks with mixed time-varying delays. Neurocomputing 73(1–3):542–551Google Scholar
- 37.Rulkov NF, Sushchik MM, Tsimring LS, Abarbanel HD (1995) Generalized synchronization of chaos in directionally coupled chaotic systems. Phys Rev E 51(2):980Google Scholar
- 38.Tang Z, Park JH, Feng J (2017) Impulsive effects on quasi-synchronization of neural networks with parameter mismatches and time-varying delay. IEEE Trans Neural Net Learn Syst 29:908–919Google Scholar
- 39.Wang L, Zou X (2002) Exponential stability of Cohen–Grossberg neural networks. Neural Netw 15(3):415–422Google Scholar
- 44.Yu J, Hu C, Jiang H, Teng Z (2011) Exponential synchronization of Cohen–Grossberg neural networks via periodically intermittent control. Neurocomputing 74(10):1776–1782Google Scholar