Local control of an array of the globally coupled oscillators

Abstract

Two control methods for stabilization of the steady states of the globally coupled second-order oscillators via local feedback are described. The first technique is based on the proportional feedback with a constant adjustable reference. The second technique is an adaptive one, employing the first-order stable filter. Three different types of oscillators have been considered: (1) strongly asymmetric version of the FitzHugh–Nagumo oscillators, (2) the classical FitzHugh–Nagumo oscillators, and (3) the van der Pol oscillators. Numerical simulations have been performed for all three types of oscillators. Detailed mathematical analysis and hardware experiments have been carried out with the asymmetric FitzHugh–Nagumo oscillators.