Synchronization of coupled FitzHugh–Nagumo systems via MIMO feedback linearization control

In this paper, synchronization dynamics of two FitzHugh–Nagumo neurons electrically coupled with gap junction in external electrical stimulation is studied. In order to synchronize all state variables in the neuron system, we regard the nonlinear feedback system as a multi-input multi-output (MIMO) system. Then, a MIMO decoupling feedback linearization algorithm and an adaptive strategy are introduced respectively to design the synchronization controllers for the two coupled neurons. Numerical simulations demonstrate the effectiveness of the developed methods.