Nonlinear Dynamics

, Volume 69, Issue 4, pp 2089–2096 | Cite as

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

  • Chi-Ching Yang
  • Chun-Liang Lin
Original Paper


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.


Synchronization FitzHugh–Nagumo (FHN) neuron Different external electrical stimulations Adaptive sliding mode control 



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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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department and Graduate Institute of Electrical EngineeringHsiuping University of Science and TechnologyTaichung CityTaiwan, ROC
  2. 2.Department of Electrical EngineeringNational Chung-Hsing UniversityTaichung CityTaiwan, ROC

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