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

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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.

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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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  1. School of Mathematical Sciences, Yancheng Teachers University, Yancheng, 224002, China

    Xuerong Shi & Zuolei Wang

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  1. Xuerong Shi
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  2. Zuolei Wang
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Correspondence to Zuolei Wang.

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Shi, X., Wang, Z. Adaptive synchronization of time delay Hindmarsh–Rose neuron system via self-feedback. Nonlinear Dyn 69, 2147–2153 (2012). https://doi.org/10.1007/s11071-012-0415-1

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