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Robust adaptive sliding mode control for synchronization of space-clamped FitzHugh–Nagumo neurons

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Abstract

Unlike taking the same external electrical stimulation to discuss chaotic synchronization in the literature, the synchronization between two uncouple FitzHugh–Nagumo (FHN) neurons with different ionic currents and external electrical stimulations is considered. The main contribution of this study is the application of a robust adaptive sliding-mode controller instead of the active elimination. The proposed sliding mode controller associated with time varying feedback gains cannot only tackle the system uncertainties and external disturbances, but also compensate for the mismatch nonlinear dynamics of synchronized error system without direct cancellation. Meanwhile, these feedback gains are not determined in advance but updated by the adaptive laws. Sufficient conditions to guarantee the stable synchronization are given in the sense of the Lyapunov stability theorem. In addition, numerical simulations are also performed to verify the effectiveness of presented scheme.

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Acknowledgements

This work was supported in part by the National Science Council, Taiwan, Republic of China, under the Grant NSC 100-2221-E-164-002.

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Authors and Affiliations

  1. Department and Graduate Institute of Electrical Engineering, Hsiuping University of Science and Technology, Dali Dist., Taichung City, 41280, Taiwan, ROC

    Chi-Ching Yang

  2. Department of Electrical Engineering, National Chung-Hsing University, South Dist., Taichung City, 402, Taiwan, ROC

    Chun-Liang Lin

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  1. Chi-Ching Yang
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Correspondence to Chi-Ching Yang.

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Yang, CC., Lin, CL. Robust adaptive sliding mode control for synchronization of space-clamped FitzHugh–Nagumo neurons. Nonlinear Dyn 69, 2089–2096 (2012). https://doi.org/10.1007/s11071-012-0410-6

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  • DOI: https://doi.org/10.1007/s11071-012-0410-6

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