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Pyragas time delayed feedback control has proven itself as an effective toolto non-invasively stabilize periodic solutions. In a number of publications,this method was adapted to equivariant settings and applied to stabilizebranches of small periodic solutions in systems of symmetrically coupled Landauoscillators near a Hopf bifurcation point. The form of the control ensures thenon-invasiveness property, hence reducing the problem to finding a set of thegain matrices, which would guarantee the stabilization. In this paper, we applythis method to a system of Van der Pol oscillators coupled in a cube-likeconfiguration leading to $O_4$-equivariance. We discuss group theoreticrestrictions which help to shape our choice of control. Furthermore, weexplicitly describe the domains in the parameter space for which the periodicsolutions are stable.

Non-invasive stabilization of periodic orbits in $O_4$-symmetrically coupled Van der Pol oscillators