Desynchronization of coupled limit-cycle oscillators through nonlinear output regulation

Synchronization is one of the most important phenomena in coupled oscillators. However, sometimes synchronization may be harmful and suppression of collective synchrony or desynchronization is desired. In this paper, we propose a control strategy for the desynchronization of an ensemble of all-to-all coupled Stuart–Landau oscillators. First, the desynchronization problem is redefined in the nonlinear output regulation framework. Then, we design an output regulator (stimulation) which forces Stuart–Landau oscillators (as a paradigm for limit-cycle oscillators) to track exogenous sinusoidal references with different phases. Finally, by considering some modifications, the initial version of the controller is improved to be more applicable in neuronal ensembles as an application of the desynchronization problem. The proposed stimulation is robust against variations of oscillators’ frequencies and can adapt itself with variations of the coupling strength. Mathematical analysis and simulation results reveal the efficiency of the proposed technique.