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Synchronization error bound of chaotic delayed neural networks

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Abstract

Synchronization of master–slave chaotic neural networks are well studied through asymptotic and exponential stability of error dynamics. Besides qualitative properties of error dynamics, there is a need to quantify the error in real-time experiments especially in secure communication system. In this article, we focused on quantitative analysis of error dynamics by finding the exact analytical error bound for the synchronization of delayed neural networks. Using the Halanay inequality, the error bound is going to be obtained in terms of exponential of given system parameters and delay. The time-varying coupling delay has been considered in the neural networks which does not require any restrictive condition on the derivative of the delay. The proposed method can also be applied to find error bound for state estimation problem. The analytical synchronization bound has been corroborated by two examples.

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Acknowledgments

The authors would like to acknowledge the funding support for this research work from HIR-MOHE Project UM.C/625/1/HIR/MOHE/SC/13, under University of Malaya, 50603, Kuala Lumpur, Malaysia.

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  1. Institute of Mathematical Sciences, Universiti Malaya, 50603 , Kuala Lumpur, Malaysia

    S. Jeeva Sathya Theesar & K. Ratnavelu

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  1. S. Jeeva Sathya Theesar
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  2. K. Ratnavelu
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Correspondence to S. Jeeva Sathya Theesar.

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Jeeva Sathya Theesar, S., Ratnavelu, K. Synchronization error bound of chaotic delayed neural networks. Nonlinear Dyn 78, 2349–2357 (2014). https://doi.org/10.1007/s11071-014-1582-z

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