Taming chaos in damped driven systems by incommensurate excitations

•It is demonstrated for the first time the possibility of reducing and even suppressing chaos in dissipative non-autonomous systems by additional incommensurate chaos-suppressing excitations through the universal model of a perturbed Duffing oscillator by considering rational approximations (convergents) to the irrational ratio between the chaos-suppressing and chaos-inducing frequencies.•Our theory predicts and numerical simulations confirm that the values of the suitable amplitudes of the chaos-suppressing excitation are rather insensitive to high-order convergents.•On the contrary, the number and values of the suitable initial phases critically depend on each particular convergent in order to satisfy two requirements: (1) Maximum approximation to the frustration of the homoclinic bifurcation existing in the absence of the chaos-suppressing excitation and (2) maximum survival of a relevant spatio-temporal symmetry of the dynamical equation.•Since the theoretical approach discussed in the manuscript is general, it can be applied in many other physical contexts, including Josephson junctions and electronic and laser systems.