Nonlinear Dynamics

, Volume 69, Issue 4, pp 2147–2153 | Cite as

Adaptive synchronization of time delay Hindmarsh–Rose neuron system via self-feedback

Original Paper
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Abstract

Synchronization of two mismatched time delay Hindmarsh–Rose neuron systems with self-feedback is investigated. Based on the Lyapunov stability theory and the adaptive control theory, a linear adaptive feedback controller and parameter estimation update law are proposed, and the sufficient conditions for synchronization of the two mismatched systems with chaotic bursting behavior are obtained. The correctness of the proposed methods is rigorously demonstrated. Finally, numerical simulations are employed to verify the effectiveness of the proposed scheme.

Keywords

Synchronization Hindmarsh–Rose system Time delay Self-feedback Chaotic bursting Linear adaptive control 
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Notes

Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant Nos. 11102180 and 51178157) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 10KJB120005).

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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.School of Mathematical SciencesYancheng Teachers UniversityYanchengChina

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