Anticipated synchronization and the predict-prevent control method in the FitzHugh-Nagumo model system

Abstract

We study the synchronization region of two unidirectionally coupled FitzHugh-Nagumo systems, in a master-slave configuration, under the influence of external forcing terms. In the particular region where the slave anticipates the dynamics of the master system, we observe that the synchronization is robust to the different types of forcings. We then use the predict-prevent control method to suppress unwanted pulses in the master system by using the information of the slave output. We find that this method is more efficient than the direct control method based on the master dynamics. Finally, we observe that a perfect matching between the parameters of the master and the slave is not necessary for the control to be efficient. Moreover, this parameter mismatch can, in some cases, improve the control.