Robust Fixed-Time Synchronization for FitzHugh-Nagumo Networks with Fast-Slow Time Scales

The synchronization of FitzHugh-Nagumo (FHN) networks with fast-slow time scales and parameter uncertainties is investigated. The sliding-mode control method and fixed-time control technique are combined, and then a criterion for robust fixed-time synchronization is addressed. By constructing the integral sliding surface manifolds, the dynamics in manifolds are analyzed, and the synchronization error system can be forced to the given sliding-mode surfaces via the fixed-time control law. Then the synchronization error system can be further converged to the equilibrium in a fixed time during the sliding motion phase. Subsequently, the upper bounded settling time estimation is presented, allowing it to be modulated to the fixed values independent of initial value conditions. Finally, a numerical simulation example is presented to illustrate the effectiveness of the obtained conclusion.