Nonlinear-estimator-based robust synchronization of Hodgkin–Huxley neurons

A controller is designed to synchronize two modified Hodgkin–Huxley neuronal systems under the influence of externally injected current stimulus and extremely low frequency (ELF) external electrical field. By transforming the dynamics of the synchronization error into the canonical form, a robust adaptive stabilization technique with least prior knowledge is used to stabilize the discrepancy system at the origin. Without directly affecting the other three internal states, all of the four states can all be synchronized. The construction of the designed synchronization controller is easy to achieve and independent of the exact drift function of the system model. As a promising adaptive synchronization controller, it is expected to be applied to solve other synchronization problems effectively.